The Corinthian church was located in southern Greece. Corinth was a very prosperous commercial center for the Roman empire. Corinth was known for its excesses and debauchery, kind of a "what happens in Corinth stays in Corinth" kind of mentality. The Romans had a word that meant "to corinthianize" which meant to take something decent and pure and totally debauch it. It was not exactly a nice place. Most of Paul's letters to the Corinthian church are written to address specific issues within the congregation -- behaviors, attitudes, excesses, spiritual issues, bad theology, etc.
Three things to notice in 1 Corinthians chapter 1:
1. Notice in 1:2 that the letter is to the Corinthians "and all others" -- Paul wrote it to a specific church in a specific place and time but the teaching is intended to be universal.
2. 1:10-17 -- the church has struggled with factions. There is a party spirit within the congregation (not a let's party -- but political party spirit). They a divided around who brought them to faith -- Paul, Apollos, Cephas (Peter) and the Christ party. These factions are pulling the church apart.
3. 1:22-23 -- preaching the crucifixion of Jesus Christ has some awkward responses from the general public. The Jews consider the crucifixion a "stumbling block" the OT says "cursed is anyone who hangs on a tree" and so the Jewish listeners cannot reconcile the message of grace with someone who has been cursed. The Greeks consider the preaching of the cross to be foolishness. In Greco-Roman culture, crucifixion was the worse kind of execution and was not spoken of in polite society. For a preacher of faith to stand up and INTENTIONALLY speak of some one's crucifixion would have been consider is the poorest of taste (a foolish thing to do).