Our "remission of sins" means not merely that we have repented, but that our sins have been forgiven by God!
Paul explains in a wonderful teaching in Romans 6, that when we were baptized into Jesus Christ we were baptized into Jesus' death, Jesus' burial, and Jesus' resurrection. Your baptism immerses you into Christ's own body which died. As Jesus was crucified, our old bodies of death are likewise destroyed.
The custom with dead bodies is to bury them, and so when you are plunged beneath the water it is as if you were buried. Notice that you cannot baptize yourself, just as a dead body cannot bury itself. And just like we die and are buried with Christ, we also are brought up out of death, out of the water, into a body which has been reborn into a brand new life! This is why we say we're all part of the body of Christ.
When we die with Christ, we die eternally to sin. When we live with Christ, we live eternally to God.
Jesus' death and resurrection is our own guarantee that our death to sin will also result in a very real physical resurrection. Because we are dead to sin, sin no longer has the right to rule over us. And because we are alive in Christ, we are now free to serve Him in righteousness forevermore.