Scholars believe that this letter is the oldest one that we have that was written by Paul. As such, it is the oldest piece of Christian literature that we have. For example, evidence indicates that it is dated at about 50 CE, twenty years before the Gospel of Mark would have been written.
His audience lived a long way away from Jerusalem--not only in miles. They were Greek and they were Gentile. Paul begins his letter, as was the practice of the time, with a greeting. But, he changes the greeting from what they would have been accustomed to.
The Graeco-Roman practice of the time was to begin letters with the Greek word, chairein, which meant "Greetings." Paul instead used the Greek word, charis, which sounds similar but mean "peace." This term would thus echo the term customarily used as greeting by the Jews, shalom, which meant "peace."
Thus, in his greeting, Paul has combined the traditonal Graeco-Roman form of greeting with the religious one. He's speaking to people who have accepted the faith and have been incorporated into God's family.
In verse 3, Paul expresses thanks to God for the way that the Thessalonians are living their lives. They have faith--not just an attitude, but the God-given power to do Christian work. They have love--not just an emotion, but the means by which they carry out this work. They have hope--not just optimism, but a confident expectation that God will triumph.
Hear the echo, in verses 9-10, as Paul describes the Christian experience. Because of your faith, you turned to God. Because of your love, you served God. Because of your hope, you are waiting for his Son, our rescuer.
(Note: my source for this explanation comes from The People's New Testament Commentary, by Boring and Craddock. I hope you have access to a copy yourself.)
Lectio Divina: 1 Thessalonians 1:2-3.