Action video games focus on exciting or challenging activities. They are a call to "action", to play your part in exciting events that require hand-eye coordination, good timing, quick reactions and learned skills.
Commonly you will control a character to navigate a level, collect objects, avoid obstacles, and battle enemies. Equipment in the game can help progress. There will be certain points in the game where the action reaches a crescendo, perhaps with a harder "boss" enemy that must be defeated before moving on.
As opposed to Turn-Based games, that pause while the player decides their next move, action games are usually time-pressured.
In Sports games this action is focused on team or individual performance in rounds of play. In Open World games the action arises through encounters with situations and characters. In platform games the action focuses on exploration and timed jumps.