The personality changes shown by a man when talking or dealing with his significant other, usually characterized by change in voice inflection and tone, as well as being more well behaved in general. This is typically only shown when the man is involved in a serious, committed relationship, but some men (usually fake, sweet talking men...aka "players") always become relationship george when talking to any woman they are trying to score with. The name george is to be interchanged with the man's actual name. This term comes from the popular TV show Seinfeld and is personified when George's fiance, Susan, begins to hang out with Elaine as a friend.
friend: "Who were you on the phone with?"
man in the relationship: "Oh that was Lisa. I just had to let her know my plans for tomorrow. We are suppossed to go out to dinner."
friend: "Yeah I could tell you were relationship Tom so I knew it was a woman."
George on Seinfeld - "You don't understand. There's relationship George, and then there's the George you know. Baudy George, Funny George."