What does "dying to self" mean?

To me, dying to self means giving up my own wants and desires for what God has for me. Changing my agenda to line up with his will for my life. I believe that one of the most powerful scriptures for this would be, Matthew 26:39 where it says, He went a little farther and fell on his face, and prayed saying, "O My Father, if it is possible, let this cup pass from Me; nevertheless, not as I will, but as you will." Matthew 6:10, when the disciples asked Jesus to teach them to pray, he said, pray thusly, Our Father in heaven, Hallowed be Your name. Your kingdom come. Your will be done on earth, as it is in heaven. Give us this day our daily bread. And forgive us our debts, as we forgive our debtors. And lead us not into temptation, but deliver us from evil. For yours is the kingdom and the power and the glory forever. Amen.

I have never heard this phrase so I am afraid I can't help you. What context is it usually used in?