An unthinking or insane leftist -- in other words, most modern leftists.
Moonbat can also be used as an adjective,
e.g. a moonbat professor. According to the
Wikipedia entry for moonbat, the word was coined in 2002 by the Editor of Samizdata, Perry
de Havilland, and was a variation on the name of radical
British activist and columnist
George Monbiot.
Originally, the term "moonbat" was intended to be more politically neutral, and described wackos on the
left and the right, but it quickly acquired its current usage of being applied almost exclusively to those on the
left.
The term also references the moon much in the same
way that "lunatic" refers to the insanity-causing powers of the full moon (
luna = moon). Bloggers occasionally analyze the behavior patterns of various moonbat "species" as if they were actual animals, and even give them satirical Linnaean taxonomical names, such as "moonbattus berkeleyensis".
The entry in the Samizdata glossary indicates that Perry originally coined the full phrase "barking moonbat"; apparently "moonbat" is just a subsequent shortened version of "barking moonbat," rather than being a pre-existing term that was lengthened to barking moonbat.
Worker #1 "Did you
see those moonbats on the news staging another one of their
useless protests?"
Worker #2 "Yeah, all
eight of them."
Worker #1 "Man, they need to get real jobs."