If someone offers a gambit, they are generally offering or allowing their opponent to take a pawn. Players do this when they feel they gain some kind of compensation for the loss of material, ie, in taking the pawn their opponent allows a strong move, or the gambiteer gains quick development or some other advantage.
An example, Queens gambit
1.d4 ..d5
2.c4 ..dxc4
In this example white removes blacks control of e4, allowing him to play e4 on the next move
3.e4
Now, if black wants to keep the pawn he has to move another pawn instead of developing a piece. On the other hand white has more space, has cleared the diagonals for his bishops and is attacking the black pawn on c4.
If you want to see some games played with the queens (or any other) gambit, check out chessbase.com or chessgames.com. Select an opening from the list which ends in gambit 🙂
Hope that helps 🙂¬~
James