A Vision of Paradise
2Cor 12:1-4 I must go on boasting. Although there is nothing to be gained, I will go on to visions and revelations from the Lord. 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. And I know that this man-- whether in the body or apart from the body I do not know, but God knows-- was caught up to paradise. He heard inexpressible things, things that man is not permitted to tell.
In competing against false teachers, Paul has been boasting of his credentials. Though he says he shouldn't have to. He has been deriding the Corinthians for their allegiance to false teachers on the basis of such teachers vain credentials, mere idle boasts. While through these last couple of chapters Paul has spoken of his superior credentials, though reluctantly.
It may be the case that such false teachers had boasted of visions from God. Paul writes to the Colossians, "Do not let anyone who delights in false humility and the worship of angels disqualify you for the prize. Such a person goes into great detail about what he has seen, and his unspiritual mind puffs him up with idle notions." Col 2:18 Here Paul says he also experienced visions, but speaks with much more humility and purposely does not go into details. Such visions would tend to invoke pride, of which Paul will speak of in the next few verses, and as such he is being careful here to suppress any sense of pride, even speaking in the third person of himself. And he is careful to admit what he doesn't know.
Beware of the kind of rhetoric you use when you speak of having a revelation from God. For sinful human pride characteristically finds a way to express itself.
But as for the particulars here:
Fourteen years ago
It is interesting that in Galatians 2:1 he had just spoken of his conversion and then said, "Fourteen years later I went up again to Jerusalem, this time with Barnabas." And there to confront the cult of the circumcision. Could be that his confrontation in Jerusalem and this letter to the Corinthians occurred the same year, in which case the vision occurred early on in his conversion.
The Third Heaven
This simply refers to what we normally call "heaven" as where the Father resides as is used in such expressions as "Our Father in heaven". The second heaven then is the abode of the stars, and the first the atmosphere.
Paradise
A bit of speculation here. To the man on the cross who died next to Jesus, the Lord said, "Today you will be with me in paradise." Luke 23:43 Yet where was Jesus that day? He was not in heaven. For he would not ascend to his Father in heaven until 40 days after his resurrection. In Acts chapter two Peter speaks of Jesus being in the grave saying, "His soul was not left in Hades, nor did His flesh see corruption." Then he spoke of Christ's resurrection. But prior to his resurrection Jesus was in Hades. Jesus described Hades in Luke 16 as a place of the dead divided into two parts separated by an impassable rift. One side was pleasant (we shall call "paradise"), and the other when we typically think of as "hell". Now what may have happened is when Jesus rose from the dead he open the gates of paradise, having atoned for sin, and essentially relocated paradise to heaven. Thus today we speak of Christians dying and going to "heaven", whereas prior to Christ's resurrection they spoke of people dying and going to "hades", also called "sheol".