There are (at least) two points of considerable interest in this great chapter.
First, “What is the third heaven of verse 2?” The general view is that the Jews knew of three heavens as revealed to them in Scripture. The first is the atmosphere or sky wherein the clouds dwell and the birds fly (cf Gen 1 :20; 2 Sam 21:10). The second was the realm beyond the first wherein dwell all the celestial bodies (Gen 1:14ff; Deut 10:22). These two heavens are joined and spoken of as “the heavens” in Genesis 2:1 and Psalm 19:1-6. The third heaven was the dwelling place of God (cf Gen 24:7). So, it is believed that Paul was somehow made privy to the glories of heaven. Given Paul’s own time frame (“fourteen years ago” – v 2) and the generally accepted date of writing (AD 57), scholars place Paul in Antioch during the earliest days of his time as a Christian. I have heard some speculate or ask if Paul was caught up to heaven at the time of being stoned and, being thought dead, was dragged out of Lystra (cf Acts 14:19-20). If the historians are correct, this would be later than the time of this vision.
There is a second explanation that I was heretofore unfamiliar. Adam Clark cites Schoettgen, whom Clarke claimed “exhausted the subject,” that this expression meant no more than Paul being brought to the highest levels of inspiration, being “favoured with the nearest intimacy with God, and the highest revelations relative to His will.” It is worth noting that the text in no way indicates that Paul was eyewitness to anything, but only permitted to hear things that he was not permitted to repeat.
Second, “What was Paul’s thorn in the flesh?” Once again, the text is not specific, noting only that it was “a messenger from Satan” to keep him humble because of the abundance of divine revelations. Many have speculated that this thorn was some type of eye malady. Paul spoke of the Galatians’ willingness to pluck out their own eyes to give to him (Gal 4:15). Moreover, Paul spoke of writing to them with large letters (6:11). Much of Paul’s writing was not done in his own hand, being dictated to an amanuensis (e.g., Tertius – Romans 16:22). Paul was careful to note the things written in his own hand (cf 1 Cor 16:21; Col 4:18), the salutation serving as the sign or proof in every epistle (2 Thes 3:17). But such is only conjecture.