Paul mentions this in 2 Corinthians 12:
So to keep me from becoming conceited because of the surpassing greatness of the revelations, a thorn was given me in the flesh, a messenger of Satan to harass me, to keep me from becoming conceited. 8 Three times I pleaded with the Lord about this, that it should leave me. 9 But he said to me, “My grace is sufficient for you, for my power is made perfect in weakness.” Therefore I will boast all the more gladly of my weaknesses, so that the power of Christ may rest upon me. 10 For the sake of Christ, then, I am content with weaknesses, insults, hardships, persecutions, and calamities. For when I am weak, then I am strong. (2 Corinthians 12:7-10)
There has been a lot of speculation about what he meant by the “thorn … in the flesh”. Some have suggested it was poor eyesight (perhaps suggested by Galatians 6:11), others have speculated that he suffered from malaria.
However, if the passage is read carefully, Paul explains what he means. He describes this affliction as “a messenger of Satan to harass me”, and he puts it in the context of “weaknesses, insults, hardships, persecutions and calamities”.
To understand what persecutions he was referring to, and who Satan was, we need to see what had happened to Paul over the previous few years. He wrote 2 Corinthians in about AD55. Four or five years earlier, he had been on his second missionary journey when he was severely persecuted in Macedonia (especially in Philippi, Thessalonica and Berea) — see Acts 16:16-17:15. He had to flee from Thessalonica in fear of his Jewish opponents. Later he wrote to the Thessalonian believers
But though we had already suffered and been shamefully treated at Philippi, as you know, we had boldness in our God to declare to you the gospel of God in the midst of much conflict . . . But since we were torn away from you, brothers, for a short time, in person not in heart, we endeavored the more eagerly and with great desire to see you face to face, because we wanted to come to you–I, Paul, again and again–but Satan hindered us. (1 Thessalonians 2:2,17,18)
Satan is obviously the Jewish opponents in this case. Looking back, Paul said
For even when we came into Macedonia, our bodies had no rest, but we were afflicted at every turn–fighting without and fear within. (2 Cor 7:5)
Having fled Macedonia, Paul stayed in Athens.
Therefore when we could bear it no longer, we were willing to be left behind at Athens alone, and we sent Timothy, our brother and God’s coworker in the gospel of Christ, to establish and exhort you in your faith, that no one be moved by these afflictions. For you yourselves know that we are destined for this. For when we were with you, we kept telling you beforehand that we were to suffer affliction, just as it has come to pass, and just as you know. For this reason, when I could bear it no longer, I sent to learn about your faith, for fear that somehow the tempter had tempted you and our labor would be in vain. (1 Thessalonians 3:1-5)
Twice he says “when I could bear it no longer”, suggesting he was struggling psychologically with the continuing persecution. After Athens, he went to Corinth. About that period of his life he says
And I was with you in weakness and in fear and much trembling. (1 Cor.2:3)
For we do not want you to be ignorant, brothers, of the affliction we experienced in Asia. For we were so utterly burdened beyond our strength that we despaired of life itself. (2 Cor 1:8)
In fact, he was so depressed by the difficulties he faced that it seems he stopped preaching altogether. While he was in Corinth, the Lord appeared to him and said
“Do not be afraid, but go on speaking and do not be silent, for I am with you, and no one will attack you to harm you, for I have many in this city who are my people.” (Acts 18:9-10)
Perhaps he was suffering from post-traumatic stress disorder.
When these passages are seen together in their chronological order, the identity of Paul’s thorn in the flesh seems clear: it was the persecution he received from his Jewish opponents. Although he prayed for relief, the Lord wanted him to endure for “my power is made perfect in weakness”. Paul recognizes this when he says
Indeed, we felt that we had received the sentence of death. But that was to make us rely not on ourselves but on God who raises the dead. (2 Corinthians 1:9)