You can read the text here.
In this section Paul writes very personally to the Thessalonians. It's overflowing with love and concern for their spiritual well being. Paul missed the Thessalonians very badly and really wanted to visit them, but Satan blocked his path. Not only did Paul care about them, but they also were the evidence of how well he fulfilled his calling before God. If they remained faithful, then he was faithful to his calling and would be deemed victorious by God on the last day. The positive report he had heard buoyed his confidence that he would be vindicated.
Paul wanted to come himself, but when he couldn't make and also couldn't wait any longer he sent Timothy, who was well known to the Thessalonians to check in on them and to encourage them to stay faithful to Jesus. Following Jesus changed a lot of relationships for the Thessalonians and made participation in the common life of their city difficult. This was something Paul warned them about. They were each others family now, and so was Paul, from whom they were separated. It was hard on both of them. He knew it would be hard, so he sent Timothy to encourage them and to find out how they were doing.
Timothy brought back good news. The Thessalonians had stayed faithful, and were full of love for one another and for Paul. This news brought Paul much relief through the trials he continued to face as he traveled around proclaiming the gospel, joy that he regularly expressed in prayer on their behalf. He also regularly asked God to allow him to return to see them once again.
Paul then shifts into a prayer of thanksgiving where he also prays for continued growth on the part of the Thessalonians. While Paul was not there long, he gave the Thessalonians a pattern of love to follow (a pattern he continued to demonstrate in this letter), and he urged them to follow it. Their love was the demonstration of their loyalty to Jesus and would bring about their vindication on the last day.
For one additional note. Gaventa has some nice comments on applying the passage on pp. 47-48. I want to quote a couple here as they are worth reflecting on.
"...this text emphasizes the vulnerability of the Christian preacher or teacher. The connection forged with those who are congregants or students is such that church leaders are themselves highly susceptible if those in their "charge," so to speak, turn aside." (p. 47).
"Paul may be speaking hyperbolically when he says "we now live, if you continue to stand firm," but he reveals something central to Christian faith and life. This is not an arena in which the rejoinder, "What I believe is my own business! can be recognized and respected." (p. 47-48).
"Because of God's actions, the apostles and the Thessalonians are irretrievably connected with one another." (p. 48).
 Both Gaventa and Fee underscore this point very well.
 Gaventa deems Paul's confidence to be profoundly bold.
 So Malherbe.
 Malherbe notes that Paul's emphasis on his aloneness throughout this passage signals empathy for the Thessalonians and their newly isolated status.
 All three commentaries are consistent in affirming that Paul means faithfulness throughout this section and not just faith, if understood to refer to assent only.