"He who finds his life will lose it, and he who loses his life for My sake will find it." - Matt 10:39
Giving away your life is relinquishing the things you like to do, that take time away from serving, for the things of God. He wants to use our time, lives, and resources to advance His kingdom, but often we're unavailable because of crap we're involved in that sap our energy and our time. It kind of the same concept when one is married, they give their lives (the old single lifestyle and activities that accompany it) for the spouse.