"GF" is an abbreviation which stands for Game Forcing.

It is used to note that a particular bid (whether natural or artificial) signifies to the partnership that the auction must continue at least until a game contract is reached. It is possible to go higher than game, but nobody is allowed to pass any bid below game.

Examples:

A)

1-1
3

A jump-shift by opener is a GF bid.

B)

1-2

If the partnership is playing 2/1 GF ("Two over One Forcing to Game"), then the 2 bid not only shows diamonds, but is announcing that the partnership has enough assets to reach at least game. (For such a bid, the responder would typically hold 13+ points).

C)
1-1

2-2

This bid of the 4th suit is usually treated as artificial and GF. It says nothing about diamonds, but the responder is saying that game must be reached.

Note that there is a big difference between "forcing" and GF. "Forcing" just means for that one round -- but not necessarily to game. For instance, 1-1 is surely forcing, but the partnership can easily stop below game.