A gambit is a chess opening, where something is sacrificed in order to achieve a better strategic position. Usually, the piece sacrificed is a pawn, but there are also gambits sacrificing a Bishop or Knight, like the Muzio gambit (1.e4 e5 2.f4 xf4 3.Nf3 g5 4.Bc4 g4 5.0-0) and Cochrane gambit (1.e4 e5 2.Nf3 Nf6 3.Nxe5 d6 4.Nxf7). Usually, the player who sacrifices something gains time or active piece play. A good example is the Middle or Danish gambit: 1.e4 e5 2.d4 xd4 3.c3 xc3 4.Bc4 xb2 5.Bxb2. White has two pawns less, but his bishops are places very well, looking to the opponents kingside. A very dubious gambit is the so called Halloween Gambit: 1.e4 e5 2.Nf3 Nc6 3.Pc3 Nf6 4.Nxe5?! Nxe5 5.d4.
Of course, one is not obliged to accept a gambit; often, one can decline without a problem.
The word gambit stems from the Italian 'gambetta' which means: setting a trap.
Some other gambits:
Smith-Morra Gambit: 1.e4 c5 2.d4
Blackmar-Diemer Gambit (BDG): 1.d4 d5 2.e4 xe4 3.Nc3 followed by 4.f3
Staunton Gambit: 1.d4 f5 2.e4
Budapest Gambit: 1.d4 Nf6 2.c4 e5
Scotch Gambit: 1.e4 e5 2.Nf3 Nc6 3.d4 xd4 4.Bc4
Queen's Gambit: 1.d4 d5 2.c4 xc4 - is the most played "gambit", but it is technically not a gambit, since white can always win his pawn back.