Anarchy is technically only the absence of government. This implies nothing about order or chaos; technically speaking, since there's no greater universal sovereign, states exist in a state of anarchy - that is, if Bulgaria has a beef with Turkey, there's no court or government to provide rules or figure shit out for them; any rules or anything like that are only there by social agreement, and there's nothing really binding states to their commitments.
When people say that they're for anarchy, they mean that they're for abolishing states. Anarchists, therefore, advocate for a society in which there is no law. Most people predict this leading to chaos, and I would agree with them. Some people think that people would get along just fine without law, however. The idea is that people will pool their resources for the shared things that they need; basically, groups of people who need roads will build roads, rather than governments. Criminals will basically be dealt with through vigilanteism, and nobody will commit crimes because they know everybody else will turn on them for disturbing order. Basically, it's a political philosophy for people who willfully ignore everything that they know about people.