The term dying to self or denying oneself has its roots from Scripture. During the ministry of Jesus, a rich young man asked Him what to do to inherit eternal life, claiming he has already done everything stated in the Law. Jesus responded that he should give all his riches to the poor and then follow Him. Sadly, the young man turned away sorrowful.
Dying to self means you are giving all the priority to God. He alone has the authority to decide, to dictate and delegate tasks that He wants you to do. The Apostle Paul sums it very clearly when he was already crucified with Christ, and although he was still living, it was not him, but Christ living in him.
It also means taking up your cross daily. It means following Christ is never easy, and only gets more difficult as you move towards the finish line.