Someone who keeps themselves to themselves, generally ignoring other people. Just as asexual = without sex, asocial = without socilisation. These asocial people tend to be on the autistic spectrum. They are perfectly healthy, they'd just rather not socialize and frankly, judging from the behaviour of a lot of students at school, I can't say I blame them. The asocial individual DOES NOT commit anti-social behaviour. They just ignore everybody.
Not to be confused with antisocial
They called Tom anti-social but in actual fact, he was just asocial. He didn't hurt a fly, he just wasn't that interested in people.