Action is about conflict. Whether with guns, blades, fists, or mysterious powers, these anime feature characters in combat - either to protect themselves or the things or people they value, or simply as a way of life.
A harem includes three or more characters who potentially show romantic interest in a male protagonist. The sex, gender, or orientation of the harem members is irrelevant as long as they exclusively, or at least primarily, are vying for the affections of the same individual - who may or may not reciprocate towards one, several, or none of these romantic rivals.
These anime showcase the joys and hardships of falling in love, whether a schoolgirl has an unrequited crush on her senpai, a Love Triangle occurs within a group of friends, or rivals become lovers through competition or their intense passion for each other.