I just came across the term "HM Slave" in reference to a Pokemon character. A couple of questions such as this one reference the term but I haven't been able to find anything that defines it.
What is an HM Slave?
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Though the necessity varies between generations and games, the general idea is that, especially late in the game, you cannot reach certain areas without some of the HM moves: i.e., strength, cut, surf, whirlpool, dive, etc. (Again, the actual requirements vary by game).
An HM slave, then, is a term for a pokemon that is not used for battle but knows one or more of these moves, such that the battle performance of your other 5 pokemon is not diminished by "wasting" one of your 4 attack moves with an HM move (which are generally subpar compared to other, similar, options).