White chooses to play an aggressive game. By giving a two-pawn material advantage to his opponent, Black spends two moves to capture both of the pawns, and has to deal with a massive attack. Black has few choices here:

• The most common move for Black to play here is to take the pawn, 3...dxc3.
• However, another common alternative is to safely decline the gambit and play 3...d5 or 3...d6.
• It's also possible to safely decline the gambit with 3...Nf6 (intending to transpose to the Ponziani after 4. e5 Nd5 5. cxd4 d6 6. Nf3 Nc6) or 3...Nc6 (leading to an independent line after 4. cxd4 d5 5. e5 f6! or the Göring Gambit of the Scotch Game after 4. Nf3, which can still be declined with 4... d5 or 4... Nf6)
• Another way to "accept" the gambit is 3...Qe7, which has recently been suggested by computers.

1. e4 e5 2. d4 exd4 3. c3

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Wikipedia has related information at Danish Gambit

• Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.