What does laying down your king mean?

Answer 1

When a player lays his king on its side, it indicates that the player is surrendering (or resigning) the game. It is not necessary to lay one's king on its side in order to resign. It is just a symbolic gesture. Fighting to the end is the best way; you never know, your opponet MIGHT make a mistake.

Answer 2

That you resign the game and your opponent wins.

Answer 3

Capitulation , "I concede the game." , Stalemate , Checkmate .