The question is based upon the knowledge that one has of a need for salvation. Sin causes spiritual death, separation from God, and the need for forgiveness from God. The Response of Faith We must believe that Jesus is the Son of God, and that He is Lord. The jailer was told this is what he must believe if he wanted to be saved. Yet, this is only part of our response.
Biblical faith is more than just believing in Jesus.
It is trust. It is taking God at His word. Once we hear what God's word has to say, we must choose to believe it and act upon it precisely because it is His word. If we recognize that we are sinners and respond to the word of God through faith, then we must make a decision to turn from sin and strive to live according to His word. He does not want us to continue living a life that is opposed to His will for us.