What does 2 Corinthians 1:11 mean?

Paul has praised the Father of all mercies and the God of all comfort for, in part, delivering him and his companions from a situation in which they seemed as good as dead (1 Corinthians 1:8–9). In addition, Paul has praised God for the comfort He gave through their suffering, a comfort he is now able to share with the Corinthians (1 Corinthians 1:7).

Now Paul references prayer. Depending on how this is translated, he either directs the Corinthians to pray faithfully for him and his co-workers, or he makes the statement that they had already been praying. In either case, Paul insists his deliverance from the near-death experience, given by God, was made possible by the prayers of many people to God on behalf of himself and his friends.

This, again, is seen as a benefit of their suffering: many people knew about their situation, prayed to ask for God's help, and have now seen God's answer to their prayers. As a result, all those people have opportunity to thank God for answering their prayers.

To be clear, Paul never expresses his desire to suffer. He does not sound like he wanted, or would want, this terrible thing to happen to him and his companions, whatever it was. He has simply shown that suffering is part of life for all people and especially for those who serve as Christ's representatives. He has expressed several benefits of his suffering, including this one: If he and his friends had not suffered in this way, people would not have prayed for them. Because he and his friends suffered, people prayed and will now give thanks and glory to God for answering their prayers.

Paul makes a point of noting that the Corinthians were part of the eventual success. They joined in this God-glorifying event through their own prayers.