The name given to the player who's controller is plugged into the first slot on a video game system. This title is usually only given out during a multiplayer game. Such a title is almost always argued/fought over, as it holds an unspoken degree of authority with it. Player 1 is usually chosen by allowing the best player or owner of the system to take this position.
"Hey, give me the 1st controller!"
"No! It's my system"
"But you suck at this game"
"Why does it matter?"
".... it just does"
Player 1 is the name that the player's controller slot which is plugged into the first controller slot is given. Player 1 usually has choice and priority over the other players, and is usually given to the person who owns the game. Even I always try to be player 1. If not, then I go for player 2, then three, then four. Not many games exceed more than four players, but I'll always go for the one closest to port 1.