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?
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).