A Skill is a special ability usable by a player character (or sometimes even a monster) in-game. In the Diablo series, all classes have distinct unique skills, and (in the first game), a shared library of spells. In the second, third, and fourth games, all skills are class-specific.
The total number of skills a character may possess is usually limited, however, usually they may improve their chosen skills by various means. The exact mechanics depend on the game which they are presented in.