The "Copy Ability" has many forms, but is easily recognizable. When a character obtains new powers or weapons by stealing or copying them from their enemies, they are displaying some form of this ability.
Some of the most notable occurrences of this concept can be found in Kirby, which often (but not always) has the power to duplicate his enemies moves after inhaling them, or Mega Man, who's signature ability is to steal weapons from the other robot masters after defeating them.
Another common place to find the copy ability is in fighting games, most of which tend to have at least one character with a version of the power, be it in the form of transforming or replicating an opponent's fighting style ( Shang Tsun) or incorporating bits and pieces of various fighters into his standard style ( Seth).
Keep in mind this concept is for characters that are actively copying powers through some special ability or artificial means, not just similar, clone-type characters. Many characters in Street Fighter, like Ken or Sakura share moves with Ryu, but are not "copying" him in the same manner as Seth.