Some people call them "antagonyms"; others call them "contronyms", or "contranyms", or (the ugliest of these labels) "autoantonym". These words are a whole lot of crazy fun to play around with.
Let me give you an example: the word "stay" can mean (a) "be in a place temporarily" (e.g., I stayed at a hotel for a couple of days); and it also means (b) "be in a place long-term" (e.g., I wasn't sure whether to accept the new job offer, or to stay at my current company).
So, antagonyms have more than one meaning, and their meanings are the opposite of each other.
Here are some more fun examples:
> reservation (to confirm you want to do something; to think twice and reconsider doing something): "I made a reservation to stay at the hotel all week." versus "I had reservations because of that hotel's bad reviews on TripAdvisor, so I'll phone some other ones."
> clip (to attach something; to detach something): "I clipped the receipts to my expenses claim." versus "Farmers clip their chickens' wings so that they can't fly away."
> assume (to suppose without knowing the full facts; to begin a new job): "Hillary Clinton assumed she would be elected president, but instead it was Trump who, in January 2017, assumed the presidency."
> oversight (careful attention; careless inattention): "Bernanke was commended for his judicious oversight of the Federal Reserve during the 2008 crisis." versus "I'm sorry I forgot to attach the document to the email - it was an oversight."
> presently (right now in the present; in the near future): "Rafa Nadal is presently the world no.1 male tennis player in the latest ATP rankings." versus "I'm stuck in traffic right now, but I'll be at the office presently."
There are lots of these in English. Do you know any? Share them with us here.
Here are a few others that I've come across, which you might know - do you know the meanings of these antagonyms?: quite, apparent, left, rocky, seeded, shelled, to dust, to sanction, to cleave, to cite, to skin, to cut, to trim, to scan, anxious, transparent, buckle, bound, sick.
(Btw, there are also some nice antagonymic phrases in English, for instance "It's all downhill from here!" I do hope many of you are inspired to participate in this discussion, and either way, well: it's all downhill from here!)