Harem is an entertainment-related trope which is characterized by three or more characters, normally female, who for some reason are in the presence and under the influence of one character, generally male, according to a few genre-defining guidelines; here it will be assumed, for simplicity of language, that the harem lead is a male character and the members are female characters. Though that is the rule, there are exceptions; a story in which there is one female character and several male characters is normally called a "reverse harem", or sometimes also "male harem". Aside from the swapping of the characters' genders, the trope's details are mostly the same, with the majority of the changes relating to the differences in behavior between men and women of the characters' age range. It is also possible to create harems with homosexual relationships, again with very few changes to the main antics themselves. The harem may not have more than only one lead, as that would be a love polygon, or less than three members, as one would form a couple and two would make a love triangle.
As a defining rule of harem, the interactions between the lead and each of the individual members are filled with romantically or sexually loaded content, either implicitly, through innuendo or subtext, or explicitly, through text or actions, and those actions are a key plot element. Generally, the female characters' looks and personalities will vary a lot among the ones present in one single series, but quite rarely will they actually differ from the common stock archetypes, which are known, well-defined, and easy to copy; for this reason, the genre as a whole is often considered repetitive. Usually, the characters involved directly in this trope are in the late teenager to young adult age range, but that is not mandatory. Sexually charged behavior on the lead's part pretty much can't be avoided, and it's typical to see him stamped as a pervert by some or all of the members, regardless of whether he is one; the sexual tones also applies to the depiction of the harem members, often leading the genre to labeled sexist. The lead will often suffer very violent retribution for his behavior, which has attracted criticism of gratuitous violence as well.
Most of the harem members will be romantically or sometimes sexually interested in the one male character, and in him alone; that, however, is not an absolute rule, and indeed sometimes none of the female characters are really interested at first, so the protagonist has to build relationships with them from scratch. That idea comes in large part from visual novels; it is quite common for visual novels to revolve around controlling the male lead and have him build relationships with either as many female characters as possible or with one of them, the latter being more common for visual novels with branched story paths; a large portion of those visual novels also feature erotic content, which may be hard to adapt to TV series. It may be also possible that the harem is only a support to the existing or predictable relationship between the lead and the most important member; additionally, the lead may end up in relationships with most or all of the harem members, with the agreement of all, in a setting normally called "harem ending".