The word TERF (or terf) is a slur that is used predominantly by transgender activists and their allies against people who criticize the transgender movement on the basis of feminist concerns. Since the slur is used for people with feminist concerns, the main target tend to be women. As such, it's usually understood to be an anti-feminist, sexist and misogynist slur.
The word was invented as an acronym for Trans-Exclusionary Radical Feminist, where the "trans-exclusionary" part referred to those holding roughly the position that transwomen should not be included under a feminist definition of womanhood, and the "radical feminist" part was meant neutrally, i.e. for people who would indeed describe themselves as radical feminists in the true sense. Over time, the acronym pretty much became a four-letter word. Nowadays the capitalization is frequently omitted, and the already ambiguous original meaning ignored entirely. Still, users of the term tend to claim that it's a neutral description. The "trans-exclusionary" part may now refer to anyone who thinks transwomen should not have unfettered access to all female-only spaces (e.g. changing rooms), should not partake in women's sports where they have unfair advantages, should not be considered a natural part of the lesbian dating pool, etc. Although most members of the public would see these as rather sensible positions, considering a "transwoman" may have intact male anatomy, transgender activists nevertheless see all of these types of "exclusion" as unacceptable.
A closely associated term is SWERF, which is supposed to stand for Sex-Worker-Exclusionary Radical Feminist and is used for those who see the sex industry (prostitution, pornography, etc.) as highly exploitative and sexist. Like TERF, the term is almost always applied as a slur, and to misrepresent the political position of the person it's used against. Ironically, some of those who have to face the term most commonly are women who worked in prostitution and became anti-prostitution activists as a result of their own experiences as so-called sex workers.