It is the most fundamental truth of the Christian faith (v. 1-3a). Paul is reminding them of the gospel - the good news that God has graciously saved sinners. The resurrection is of "first importance."
It is upholds the truth of the bible (v. 3b-4). Everything about the Jesus' death, burial, & resurrection is supported by scripture. Isaiah 52:13-53:12 speak most directly to Jesus as the "suffering servant." Psalm 16:9-10 echoes the resurrection. But a deeper echo of the resurrection I believe is found in Genesis 1-2 where we see God as Creator. For what does God create? He creates life, not death, which led Jesus to teach himself on the resurrection in light of God being "The God of the living" (Mark 12:26-27). Interestingly, the Jews didn't expect the Messiah to resurrect. They only believed in a corporate resurrection, not an individual one. So when Jesus resurrected, that actually cemented his claim as the True Messiah in a day when there were many so-called "messiahs' who would get caught & killed...and stay dead.
It is an historical fact (v. 5-8). There were hundreds of witnesses that Paul mentions here that he is begging the Corinthians to talk to in order to check out his story about Jesus. 1 Corinthians (along with Philippians and Colossians which contain some early creedal hymns about Jesus' deity) predates the gospel accounts of Matthew, Mark, & Luke by a decade and John by two decades. 1 Corinthians was a public document meant to be distributed and read. By going so public with Jesus' resurrection, it underlines the truth of the event. And, there is simply no other way to explain the transformation of people's lives, the explosive growth of the church, and the impact on the history of mankind if the resurrection never happened.
The core of the resurrection is grace (v. 9-11). At the heart of the resurrection is a loving God who did what we were unable to: rescue us from our sin. Sin leaves us powerless. We can't work hard enough, do enough good things, serve or give enough, be kind enough, etc to be connected to God and have the promise of heaven. So God decided out of love to show his lost children grace - giving them a blessing they did nothing to deserve. Jesus took all of our punishment and penalty for sin on the cross and then defeated death by his resurrection. That grace is what then motivates us to work, give, serve, and do good. All we're asked to do is believe it (v. 11).
I pray that you believe the truth of Jesus' resurrection. Because if (or should I say since) the resurrection is true, then everything changes. You can have real hope. You can have real healing. You can experience true transformation. If you do not have this faith in Jesus, or if your faith is struggling, all you need to do is ask God to give you faith to trust in His grace that He gave us in Jesus through his death, burial, & resurrection - the fundamental truth of the Christian faith.