The Games Master (or GM) is the person who runs a Role-Playing game. The Games master is often likened to an authour, in that she lays out the plot of the adventure that is being played. In actual fact the GM is more like God, she designs the world and the people within it, but then leaves it to the free will of the players to decide what their characters do. It is the interaction of players and GM that decides what actually happens in the course of the game.
The GM also takes the part of the physical laws of the world deciding, often with the help of dice or some other system designed to introduce a random element, whether actions undertaken by the characters in the game succeeds or fails. In general he or she will do this with the aid of a specific system
The Games Master has as many different titles as there are games. The most traditional is Dungeon Master (DM) from the Dungeons & Dragons games. More modern games often favour some variation on 'storyteller'.