Google dictionary defines "apocalypse" as:
the complete final destruction of the world, especially as described in the biblical book of Revelation.
Wikipedia gives a more complete explanation when it says:
An apocalypse (Ancient Greek: ἀποκάλυψις apokálypsis, from ἀπό and καλύπτω, literally meaning "an uncovering") is a disclosure of knowledge or revelation. In religious contexts it is usually a disclosure of something hidden, "a vision of heavenly secrets that can make sense of earthly realities". 
In the Book of Revelation (Greek: Ἀποκάλυψις Ἰωάννου, Apokalypsis Ioannou – literally, John's Revelation), the last book of the New Testament, the revelation which John receives is that of the ultimate victory of good over evil and the end of the present age, and that is the primary meaning of the term, one that dates to 1175.
Today, the term is commonly used in reference to any prophetic revelation or so-called end time scenario, or to the end of the world in general.
2 Peter 3:10-12 says:
But the day of the Lord will come like a thief, and then the heavens will pass away with a roar, and the heavenly bodies will be burned up and dissolved, and the earth and the works that are done on it will be exposed. Since all these things are thus to be dissolved, what sort of people ought you to be in lives of holiness and godliness, waiting for and hastening the coming of the day of God, because of which the heavens will be set on fire and dissolved, and the heavenly bodies will melt as they burn! ()
According to Peter then, there will be a final Apocalypse, a day when the world ends. However, this actually is not the end, but a new beginning. 2 Peter 3:13 continues with this thought:
But according to his promise we are waiting for new heavens and a new earth in which righteousness dwells. )
All unrighteousness and ungodliness will be done away with, thus in the new heavens and new earth there will be only righteousness.
Until that time, we live in a world full of unrighteousness and ungodliness. According to Romans 1:18:
For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who by their unrighteousness suppress the truth. ()
There is a "revealing" of God's wrath that is continuously going on. God's wrath was being revealed at the time the epistle to the Romans was written and it is being revealed today. This revealing is the uncovering or unveiling that the word "apocalypse" refers to, and it is a portent of the great Apocalypse to come.
Romans 1:18-32 lays out for us how God's wrath is being revealed.
God's wrath is being revealed in three stages or steps. These stages are progressive. In other words, they build on each other, and yet at the same time, all three can be observed at any given time. Throughout history, different cultures and different individuals have displayed these stages in various forms. Examples of all kinds abound; from ancient Sodom, Israel and Rome to modern Europe, Syria and America we can see all the stages of the revealing of God's wrath.
The stages are as follows:
1) God gave them up in the lusts of their hearts to impurity. v. 24
2) God gave them up to dishonorable passions. v. 26
3) God gave them up to a debased mind to do what ought not to be done. v. 28
We are going to look at these three stages in turn. However, we first need to consider the meaning of the phrase "God gave them up." The word used in the original language is defined as: "to hand over, to give or deliver over."
We see an example of "giving over" in the account of the introduction of sin into the world. God warned Adam that in the day he ate of the fruit of the tree of the knowledge of good and evil he would surely die. (Genesis 2:17) When Adam and Eve ate from the tree, God turned them over to the consequences. Their spiritual death was immediate as forewarned, but the consequences were many and complex. Disease, sickness, hardship, pain and various consequences have been revealed. These consequences are progressive, but are not revealed in the same way in every person. For example, not everyone gets cancer, but cancer exists as a consequence of sin. Not everyone is killed in a car crash, but car crashes exist as part of the consequences of sin. This is not to say that everyone who dies of cancer or a car crash is suffering for a specific sin. Rather, by choosing to sin and reject God's protection, humanity opened itself up to death in all of its horrible manifestations. The family that dies in a house fire is no better or worse than any other family. God has turned humanity over to the consequences of the choice we made to reject Him. I know I am saying horrible, atrocious things, but look at the world around us. Horrible, atrocious things happen and most of them are done by people to people. Rather than take away our freedom as responsible moral agents, God has left us free to suffer the consequences of our actions. This handing us over or giving us up is how God progressively reveals His wrath. He does this as a warning so that we can be turned to repentance. He holds back His wrath, but the day of wrath will come when unrighteousness and ungodliness are done away and all the consequences of sin along with them. It will be a new day of rejoicing and freedom for those who trust in Christ Jesus.
Therefore, God's giving over or giving up of humanity to the consequences of our sin is how He reveals His wrath.
The first giving over is explained in Romans 1:24-25. Romans 1:24 says, "God gave them up in the lusts of their hearts to impurity."
The key concept here is the lusts of their hearts. By letting our lusts or appetites rule us, we practice things that are termed impure. What is worse, we become enslaved by these things. The stronger enslavements we call addictions because as a slave, an individual has no power to say no to his or her lusts. This enslavement and subjection to our own appetites is described in verse 25 that says:
because they exchanged the truth about God for a lie and worshiped and served the creature rather than the Creator, who is blessed forever! Amen. ()
The key to understanding this first stage is here in the “worshiping and serving the creature rather than the Creator.” Our own appetites, desires or lusts become our god. This is described for us also in Philippians 3:19 when it says, "their god is their belly." In other words, we worship and serve the little "I am" (self) instead of the Great I Am (God).
Verse 24 shows us the consequences of this giving over in the statement, “...to the dishonoring of their bodies among themselves.” This is referring to sexual immorality. The inability to control our lusts shows itself in all kinds of ways but sex is where we shame ourselves. As 1 Corinthians 6:18 says, sexual immorality is a sin against our own bodies. Sex is good and necessary, and God has carefully protected and defined its boundaries as being for a lifelong covenant relationship between a man and a woman. It creates a "oneness" of soul that no other act or practice can duplicate. This is why sex is so powerful, and any other use brings heartache, grief and awful consequences. Concerning sex outside of marriage, God warns us, “Can a man carry fire next to his chest and his clothes not be burned?” (Proverbs 6:27, ESV) It may seem like we have escaped without consequence, but this is not what the Bible teaches. Immeasurable heartache, suffering and death are in the world because of this one issue.
Because humanity does not consider the consequences of stage one and because we still refuse to honor God as God, He gives us up to stage two. Stage two, like stage one, comes as a natural consequence of our stubborn refusal to acknowledge the truth about God.
Verse 26 defines stage two as, “God gave them up to dishonorable passions.”
The key concept here is dishonorable passions. The word translated dishonorable is defined: “dishonor (perceived as without recognized value, worth).” As in stage one, the "giving over" is in the passions or desires of the body, and it is also specifically related to sexual desires. There are desires for money, food, material possession, power, control and a host of other material and immaterial things in which our desires are given over. The passage talks about sexual desires, but we see the "giving over" in a myriad of ways. The progress from stage one to stage two is one of a change or growth in the desires to something that is unnatural. Verse 26 and 27 describes this change as:
For their women exchanged natural relations for those that are contrary to nature; and the men likewise gave up natural relations with women and were consumed with passion for one another, men committing shameless acts with men and receiving in themselves the due penalty for their error. ()
The Bible is clearly speaking of same sex attraction. There are two mistakes we can make here. One is to think that since we do not experience same sex attraction we are somehow free from stage two and better than those that do. The second mistake is to think that because we experience same sex attraction we are somehow worse (or better) than those that do not.
The Bible is clear that we are all tempted. What is a temptation for me may not be a temptation for you. (I have even heard of people who do not like chocolate. I cannot imagine it but it happens.) We are all affected by sin and suffer to some degree from the "giving over" of stage two. Temptation becomes sin when we cast off restraint and act upon our desires whether they be what others consider normal or abnormal. The consequences of stage two, just the same as in stage one, are catastrophic for the individual as well as the community.
Romans 1:26 terms these passions as being without value or worth. They add no value and are seen as unnatural. The fact that we have desires that are without recognized value or worth should serve as a warning to all of us of our desperate need for God.
The third and final stage is expressed in verse 28 as:
God gave them up to a debased mind to do what ought not to be done.
The key concept here is a debased mind. The word translated “debased” here is defined as: “failing to pass the test, unapproved, counterfeit.” In giving us over to a debased mind, God has turned the intellect over so that in its subjection to animal passions it has become an animal mind. Like unthinking animals, our behavior becomes totally corrupt. The list of verses 29 through 31 is ugly.
They were filled with all manner of unrighteousness, evil, covetousness, malice. They are full of envy, murder, strife, deceit, maliciousness. They are gossips, slanderers, haters of God, insolent, haughty, boastful, inventors of evil, disobedient to parents, foolish, faithless, heartless, ruthless. ()
While I do not wish to deny the truly wonderful things that humanity has accomplished and that people do, I have to recognize that this list reads like the world news. This third stage is the state of humanity while God is holding back the evil that could be. When He takes away His restraining hand, the world will pass through the great tribulation. Seeing the evil that people perpetuate against other people should be a warning to us that God is not going to hold back the consequences of our rebellion against Him forever. Verse 32 gives the summary of how we can see the wrath of God being uncovered when it says:
Though they know God's righteous decree that those who practice such things deserve to die, they not only do them but give approval to those who practice them. ()
Rather than repenting and admitting that God is right and we are wrong, we support each other in our sin. We encourage each other, and tell each other that we are okay. Even churches get into the act. Denying the gospel, there are those that preach success or psychology or some other form of truth. 2 Peter 2:1-2 warns us of this when it says:
But false prophets also arose among the people, just as there will be false teachers among you, who will secretly bring in destructive heresies, even denying the Master who bought them, bringing upon themselves swift destruction. And many will follow their sensuality, and because of them the way of truth will be blasphemed. ()
Even here, we see that false teaching comes from "sensuality." This is more evidence of God "giving over" people to their sin, and this is the scariest revealing of God’s wrath. When those entrusted with the truth of the gospel stop proclaiming the truth and warning those who are perishing, what hope does the world have?
The day of His appearing is fast approaching. What will it take to wake us up?