I've heard two different meanings that both come back to the same basic principle.
In the Bible, Jesus said, "Greater love hath no man than this, that a man lay down his life for his friends." John 15:3
I've heard a wise woman say that if you love someone you put their happiness and their needs ahead of your own. Your greatest desire will be to make them happy.
I think those both boil down to the same thing. If you love someone, you sacrifice your wants and needs to satisfy theirs.