Hermaphrodite is a term which comes from Hermaphroditus, the son of Hermes and Aphrodite. It is used as a scientific term in biology.
In zoology, an animal which can produce both sperm and ova is a hermaphrodite. As an example, most earthworms are hermaphrodites. A simultaneous hermaphrodite has both sets of sex organs throughout life. A sequential hermaphrodite has ovaries at first, replaced by a testis later, or the other way round.[1]
In botany, hermaphrodite is used for 'complete' flowers with both male and female parts, and for plants which have bisexual reproductive units. See flowering plant sexuality for details.[2]
With people, the term hermaphrodite is not correct, because true functioning hermaphrodites are not possible in humans. What sometimes happens is errors in development which lead to intersex persons. A definition of intersex is:
People who are intersex may have a very small penis and no testicles, or a very small and short vagina and a large clitoris that looks like a penis. The term hermaphrodite is considered offensive and outdated by many intersex people.