Anti-social behaviour is behaviour generally seen as disruptive, intimidating, distressing for other people like verbal abuse, offensive behaviour. It includes low level criminality such as graffiti drug dealing, violence or threatened violence, verbal abuse, and much more. Anti-social behaviour is often the subject of legislation. Dealing with anti-social behaviour can start with warning letters and conflict resolution meetings but there can be also be legal sanctions.
A 'zero-tolerance policy' is one perceived way of dealing with ASB; likewise ASBOs.
Loud noise like loud music or slamming doors can be anti-social, so if you like loud music in the middle of the night and you don't want to get into trouble with the Law or with your neighbours, buy headphones.