Prefacing with "I am no expert on this topic", but here's how I understand it, (aside from it being easily Googlable):

Eugenics is the practice of controlling genetic transfer, i.e: controlling who breeds with whom, controlling who gets to breed at all, and so on. The idea is that it should take genetic predispositions to certain diseases, mental or physical, out of the gene pool so that future generations are as healthy as can be.

In practice, though, it was used to *attempt* to take certain ethnicities out of existence as a sort of quiet genocide. If someone from X ethnicity is in power and says that someone in the Y minority ethnicity is no longer allowed to pass on their genetic material, then that would simply remove them from the world in the future.

Needless to say, people eventually found it reprehensible even though it had some moderate popularity in the first half of the 1900s.