Action is a game category that has more accent on physical challenges, player’s coordination and reaction-time. This category includes a large number of sub-categories, such as fighting games, beat 'em ups, shooter games and platform games.
In an action game, the player typically controls a character that must navigate a level, collecting objects, avoiding obstacles, and battling enemies with their natural skills as well as weapons and other tools that he collects or has.
At the end of a level or a bunch of levels, the player commonly encounters a boss enemy that he must defeat. Usually he is more challenging than the rest of levels mobs.
Action games usually contain health and lives of the player, and the player receives a Game over when they run out of lives. Or you might just complete all levels and see the ending credits.

Early action arcade games were unbeatable and had an indefinite number of levels. Player's only goal was to get as far as they could. Usually those games were highscore games.