Herm is a shorting of the word "hermaphrodite" for purposes of tagging and search simplification.
If a character is both a complete male and a complete female, whether it is because they are naturally occurring hermaphrodites such as many plants, or because they have both male and female sex organs, then this tag is appropriate.
The tag herm typically refers to characters with both male and female primary sex organs, specifically the vulva and the penis. Although testicles are a necessary part of fully functional male sex organs, not all species (or characters) have balls, as the testes may be kept internally (like their female homologue the ovaries). While most herm characters have breasts and a female body shape, there are a rare few who do not, who get the additional tag of maleherm based on their appearance.
Following the 'tag what you see' rule, the herm tag should not be used on images of characters which are known to be hermaphrodites, but are portrayed with the male portions of their genitalia not evident in that individual picture. Crotch bulge classifies as visible for this purpose.
Futanari was a special case of the tag herm for those characters with primarily female body and a penis in place of a clitoris (a common form of hermaphrodite in hentai), but the tag now aliases directly to herm.