If you sacrifice a piece , usually a pawn, during the opening in order to achieve an advantage, it is called a gambit.
These are some popular gambits:
1. d4 d5 2. c4
White aims at controlling e4 square , wants to have pawn majority at the center and to take advantage by using c line.
2. ... dxc4 3. Nf3 Nf6 4. e3 e6 5.Bxc4 c5
or Black can decline the gambit ( Queen's Gambit Declined ).
1. d4 d5 2. c4 e6 3.Nc3 Nf6
1. e4 e5 2. f4
white aims at controlling central squares and use f line to attack. But it creats King's side weakness.
Black can play 2. ... exf4 (King's Gambit accepted) or 2. ... Bc5 (King's Gambit declined) or 2... d5 (Falkbeer Countergambit)
1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. b4
White aims at controlling central squares quickly by playing c3 then d4
Black can play ( gambit accepted )
4. ... Bxb4 5. c3 Ba5 6. d4 d6 ( or exd4)
or 4. ... Bb6 ( gambit declined ) 5. a4 a6
1. e4 e5 2.Nf3 Nc6 3. d4 exd4 4. Bc4 Bc5 5. c3 dxc3
( 5. ... Nf6 transposes into Giuoco Piano )
6.Nxc3 d6 7. Bg5 Qd7
There are a lot of gambit. Some of the others are
Marshall Gambit : 1.e4 d5 2.exd5 Nf6
Albin Counter : 1.d4 d5 2.c4 e5
Vienna Gambit :1.e4 e5 2.Nc3 Nc6 3.f4
Latvian Gambit (Greco Counter Gambit) : 1.e4 e5 2.Nf3 f5