A hermaphrodite is a being which possesses both male and female reproductive organs.
Hermaphrodite is the term used for an organism that has what would be considered both male and female reproductive organs. In nature, this happens in many snails, slugs, and plant life, and to some degree hermaphroditism can occur in animals and even humans, on rare occasions.
Hermaphrodite characters in anime and manga are usually referred to as "futanari" and are almost universally female in manga/anime. They are more often found in the hentai (ero) style of series. Typically such characters are born as primarily one gender but also with the genitalia of the other gender, with varying degrees of completeness. Sometimes the extra reproductive organs are grown artificially through magic or science.
The theme is not isolated to hentai alone and some characters of mixed gender can be found in other series that target an older teen audience. Normally for shock value of seeing a lovely woman who will later be revealed to be a hermaphrodite. One such case can be found in the manga series Battle Club.