The Budapest Gambit is a gambit because black offers a pawn on move two with the idea of gaining rapid development and attacking chances in return. White can either accept the gambit pawn with 3.dxe5 or decline it with 3.Nf3. If white accepts the gambit, black will gain a lead in development and try to use their lead in piece activity to create threats against white's position. If white declines the gambit, black will have a more solid position and will try to use their active pawn structure to gain control of the center of the board.
One of the main advantages of the Budapest Gambit for black is that it can take white out of their comfort zone and force them to play positions they may not be familiar with. The opening is also full of tactical possibilities, with both sides having opportunities to create threats and counter-threats.
However, the Budapest Gambit is not without its weaknesses. If black fails to develop their pieces quickly and efficiently, they may end up with a weak position that is easy for white to exploit. Additionally, if white plays accurately and calmly, they may be able to neutralize black's attacking chances and gain a lasting advantage.
Overall, the Budapest Gambit is an interesting and dynamic opening that can be a useful surprise weapon for black in certain situations. However, it requires careful play and good tactical awareness to be successful, and it may not be the best choice for players who prefer more solid and traditional openings.
Below is a video outlining the Budapest Gambit:
