2 I know a man in Christ who fourteen years ago was caught up to the third heaven. Whether it was in the body or out of the body I do not know—God knows.
What is the "third heaven" that Paul mentions in this verse?
Two viable and not necessary mutually exclusive interpretations can be offered which result in the same theological conclusion.
Sky, Space, Heaven
I heard R.C. Sproul suggest that first heaven would denote the sky, second heaven deep space, and third heaven the presence of God. Ted Donnelly takes this interpretation in his book Biblical Teachings on the Doctrines of Heaven and Hell:
Three is Perfect
Three is a number of perfection because of the Trinity (e.g. Isaiah 6:3) and so Paul may very well mean it to be taken in a qualitative rather than quantitative sense—i.e. not indicating that there are multiple heavens but saying something to the effect of the heaven of perfection. Calvin says in his commentary on this verse:
Either way, the safest way to understand this phrase in 2 Corinthians 12:2 is that third heaven indicates an immediate revelation of the presence of the Triune God.
I cannot provide the exact cultural implications at the moment, but the third heaven has traditionally been taken as "into the very presence of God." This certainly was the position advocated by Aquinas as well as Augustine.
In Gen 1.1 'heavens' is a dual form of the word. God created two heavens and one earth. These are heavens 1 and 2 as listed above. They are created heavens.
The third heaven is referred to as the heaven of heavens:
Even the heaven of heavens cannot contain God. There is no container larger than God. Even this third heaven is within God himself. Since those going there have an 'out of body' type experience, it is suggested that it exists in a spiritual realm.
The Jewish sages tell us that when God created, he created the void within himself, since there was no place outside of himself. Then he created what we see, within and from the void.
With this model, the third heaven is outside of the void and within God himself. While we exist in the void, there is a separation from the essential nature of God. In the third heaven, His essential nature is experienced without separation.