NEET means Not in Education, Employment, or Training. Basically someone just bumming around, no job, school, or plans.
At times you can hear Aqua call him a "shut in-NEET"(she says hiki-NEET in japanese). Hiki- is short for "hikikomori" which is a shut in. The difference is that a hikikomori is someone who shuts themselves in, *very* avoidant (for various reasons) of social interactions and the world outside of their room/house. A hikikomori can be a NEET, but not all NEETs are hikikomori.