In prior chapters of I Corinthians Paul builds up the young church by instructing them in matters such as communion, how to treat each other and divisions in the church. In this passage he continues to encourage by going back to the basics and reminding each of us about what Christ did for us.
First of all, Paul says, remember that Jesus rose from the dead. I have known about the resurrection for my entire life. I forget how exciting it was as current news, which Paul here repeats; Christ died. He was buried (in other words, He was REALLY dead). He rose. There were many eyewitnesses to His resurrection which Paul lists here, including Jesus’ half brother James (I like to think with instructions to reassure His mother that He had risen).
Then Paul lapses again into thankfulness to Jesus for saving Paul from his old life. Often I look at Paul as needing God worse than I do (since his old life had more actual violence involved), but to personalize this passage I think, what old life was I taken from ? What old life am I to be taken from daily, as I turn my day over to God? Lack of gratefulness to Christ? Unkindness? Selfish hoarding? What does it look like for me, today, to put my gratefulness to Christ into action?