Part-trolls are, apparently, beings with some, but not a total, amount of troll heritage or blood, as well as part human blood.
Part-trolls are, apparently, agressive individuals with a troll's characteristic foul smell.
Behind the scenes
It is unknown whether the term 'part-troll' describes an actual human/troll cross-breed or if it is just a derogatory phrase used to insult large, agressive, and foul-smelling wizards and witches. Given the context in which it appears in the novels (described as a "small instance of humour"), the latter is most likely.