1.d4 d5 2.c4, and that pawn on c4 is free. Black takes it with 2…dxc4 and is a pawn up before move three. White knows this perfectly well. The offer is the whole idea.
A gambit is material handed over on purpose in the opening, nearly always a single pawn, in return for something a pawn cannot buy: free moves, a bigger centre, or a file that opens for your rook while the other side is still carrying the pawn home.
8 
7 
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e f g h 1 What the pawn actually buys
Count Black’s moves in that line. Taking on c4, then b5 to prop the pawn up, then c6 to prop it again, then cxb5 to recapture: four pawn moves out of five, and not one piece off the back rank. White has a knight and a queen out, a healthy centre, and the pawn coming back anyway.
That is the trade every sound gambit is selling. One pawn for three or four free moves. Each free move has a name, a tempo, and the old rule of thumb is that three of them in the opening are worth about a pawn. Get more than three and the gambit is a bargain. Get one, and you are just a pawn down.
The Queen’s Gambit is a gambit by courtesy only
Black can take on c4 and will not be able to hold it, which makes 2.c4 less an offer than a loan. Compare the King’s Gambit, 1.e4 e5 2.f4, where after 2…exf4 the pawn really is gone and White has to prove the open f-file and the big centre are worth it. Or the Evans Gambit, 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4, where the b-pawn is thrown at the bishop to gain a move and then build a centre with c3 and d4.
Those are the real ones. You will not get the pawn back by force in either.
Playing against one
The mistake I see most in club games is not taking the pawn. It is taking the pawn and then trying to keep it with more pawn moves, exactly as Black did above. Grab it, develop, castle, and return it the moment holding it costs a second tempo. A pawn is a pawn, but a lead in the centre that turns into an attack costs far more than one.
If you want to see what a proper investment looks like once the pieces are out, the sacrifice puzzles are the middlegame version of the same bet.