Futanari (二成, 二形; ふたなり - meaning two forms or two appearances) is a term describing hermaphroditic persons or the genre of hentai depicting them. It is a broad term, often including both shemales and hermaphrodites as well as girls with so-called "clit-dicks." 
Futanari are often depicted in a number of ways, differentiated mainly by their genitalia.
The simplest futanari are often otherwise normal girls who have an oversized clitoris. (La Blue Girl is the most well-known example.) The clitoris often expands approximately to the size of a penis when aroused, but it is tapered at the base and often does not have a glans (head). It is often depicted as being quite small (about the size of a large pencil). Occasionally the plot in these stories involves a normal girl who discovers that her clitoris will "grow" into a penis (or penis-like appendage) when she is aroused. (Such as in Tiltmode.)
By far the most common type of futanari are sometimes called "the ball-less wonder." These girls naturally have a penis (or, as is common in CCS doujin and similar manga, are "magically" granted a penis) and have a vagina, but no testes - no balls. In stories depicting multiple futanari characters (such as Anal Justice), most or all are of this type, sometimes to differentiate them from boys and shemales.
Less common but popular are the true hermaphrodite. These girls have a vagina (usually with no clitoris), an (usually large) penis, and descended testes. They are often characterized with an insatiable libido. In some cases, they are magiclly or biologically made as such (as in P Total Biochemical Lab).
Least common is the shemale or new-half. Most often, these characters are male-to-female transsexuals and are often more interested in males than females. Magic is rarely a part of their creation. (The Amanoja9 and Wolf Ogami are known for their depictions of new-halfs.)
Related sub-genres include gender-bending and cross-dressing themes.
 Examples of Futanari content
The following is by no means comprehensive. See the futanari category for more.