How a chess game is drawn by the mutual agreement rule

A chess game can be drawn if both players agree to it. 

Here are the official FIDE rules:

1. A player can propose a draw after making a move on the chessboard. He must do so before stopping his own clock and starting his opponent's clock. An offer at any other time during play is still valid, but Article 12.5 must be considered. No conditions can be attached to the offer. In both cases the offer cannot be withdrawn and remains valid until the opponent accepts it, rejects it orally, rejects it by making a move, or the game is concluded in some other way. The offer of a draw shall be noted by each player on his scoresheet with the symbol (=).

In practice, there may be several reasons for agreeing to a draw, for example: