(part of common anime words)
NEET is an acronym. It stands for Not in Employment, Education or Training. That is, someone who is a NEET is someone who spends his day doing... nothing. Absolutely nothing. Because they are not employed, they have no jobs. They aren't studying, either, no school, no classes, no courses. And they aren't acquiring new skills, no training. So they do... nothing. Nothing at all.
By the definition above, any unemployed person who already finished his studies and is looking for a job would be a NEET, however, you're not a NEET just because you are Not in Employment, Education or Training, but also because you want to be Not in Employment, Education or Training.
That is, you're lazy bastard and do not contribute to society. You're useless. A leech. Scum. A NEET.
The word is clearly English, not Japanese, but it's pretty much only used in Japan. It appears to have been coined in England and used by the government in official contexts, but from anecdotal experience I can tell you people who say NEET outside of Japan most likely have heard it from anime and not in some legit English text.
Difference with Hikikomori and OtakuA NEET is not synonymous with a hikikomori 引きこもり. A hikikomori is usually a NEET, but some NEET don't even have where to hikikomoru into, so they can't be all be hikikomori.
A NEET also has nothing to do otaku オタク, though, for some reason, they are often associated with each other. They are such parallel concepts, that some people have employment exactly because they are otaku so it makes no sense to assume one is a NEET because he's an otaku and vice-versa.
To have an idea of a character who is a NEET, but is not a hikikomori and is not an otaku, think about Hasegawa Taizou 長谷川 泰三 from the anime Gintama 銀魂, also notoriously known by the affectionate nickname MADAO.
(MADAO stands for maru de dame na ossan まるでダメなおっさん, which means "completely useless old man". MADAO also stands for other things through the Gintama 銀魂 anime as a running joke.)
NEET in AnimeNEET are, justifiably, regarded a societal problem in Japan and in pretty much everywhere in the world (except they won't use the word NEET). Because of that, many anime have NEET characters, plot arcs based upon the concept of NEET, and some go as far as being entirely about NEETs.
Such is the case of the manga and anime "Welcome to NHK!" NHK ni Youkoso! NHKにようこそ！ Which shows how a severely socially anxious character lives his paranoia-filled life.