When Curse is used by a Ghost-type Pokémon, the user will lose half of their max HP and in turn will place a curse on the opponent. This curse will cause the afflicted Pokémon to lose 1/4 of their max HP at the end of every turn, unless switched out. When combined with Mean Look or Block, it can be a destructive combination. It is much like burn.
With the exception of Hidden Power, Curse is the only move that has effects that vary depending on its user.