Nightmare is the second of three difficulties found in diablo II. It is reached by killing Diablo on normal, or killing Baal on normal if you are playing the expansion.
You will receive a -50 to all resistances upon entering Nightmare, and when the monster are also increased in level, the difficulty of the game increases considerably. As monsters are higher levels, they also drop (have a chance to drop) better items, for more upon this see the respective item sections.