What does it mean to "die to self"? It's a strange phrase, but commonly used in the New Testament. Baptism is a sign of how we begin this journey. Romans 6:4 says, "For we died and were buried with Christ by baptism. And just as Christ was raised from the dead by the glorious power of the Father, now we also may live new lives". It means moving from an old way to a new way of living.
