> The man who went to the third heavens
This is generally considered to be Paul himself, trying to be self-effacing (which was typical of Greek and Jewish writers of the time) and not puffing his chest out in spiritual pride. The evidence that it is Paul is as follows:
- The Corinthians have pressured him to produce some kind of statement of qualifications, so it would make sense the experience is to be understood to be about himself.
- Verse 7 seems to be showing that he is talking about himself.
> What does this mean?
Presumably you're taking about what "the third heavens" is? It's a pretty oblique reference. It's unlikely, however, that Paul is talking about the idea of seven heavens held by some Jews. Other Jews spoke of two heavens—the visible clouds, and the sky beyond them. In that case, the 3rd heaven would be God's region beyond that. Other Jewish writers even speak of as many as 365 "heavens." He's probably not talking about different levels of heaven. A scriptural perspective, separate from Jewish tradition, is that there is one heaven (Mt. 25.19-23; Lk. 19.15-19; 2 Cor. 5.10). The most plausible interpretation is that Paul is using this vocabulary to speak about the one heaven where God is, the "3rd" indicating what is sublime. He was given a vision of God in Heaven.
> How do we understand this?
God gave Paul a visionary, ecstatic experience of Himself, something humans rarely get to see (cf. Isa. 1; Ezk. 1). Since he is most likely trying to justify his qualifications as a spokesman for God giving the truth about God and heaven, an experience like this would go far. He is telling the Corinthians that he has first-hand access to the things of God that he preaches. It's one of many reasons we read Paul's writings as have authority as a message from God.