Effectively, it means that the property can only be occupied by someone who currently works in - or is retired from - agriculture (or related rural industries such as horticulture and forestry). So, while there would be nothing stopping you buying the property, you couldn’t actually live in it!
AOCs are in fact very common - they originate when a planning application is submitted by someone like a farmer, who wants to build a house on what is otherwise agricultural land, either for his own use or for one of his workers. Ordinarily of course, such applications would be turned down, since there is a general presumption against allowing residential development in open countryside. However, they may be granted - with an AOC - if it can be proved that there is a special need. Since this is a local rather than a national planning matter, the precise nature of the AOC will vary from place to place. So, someone who works for a fencing contractor, for example, may be acceptable in one area but not in another.
Unsurprisingly, with strict limits on who can occupy such a property, the impact on selling prices can be significant – hence why the property you’ve seen looks like such a bargain!
Most Local Authorities are very reluctant to revoke AOC’s – if only to stop speculators buying up rural properties on the cheap with the aim of making a killing by selling them on later at the full market price. Even where councils are prepared to consider it, they certainly don’t make it easy - the current owner might first have to go through a full marketing exercise, perhaps for a year or more, in order to prove that there is no market for the property encumbered.
So, all in all, even if it sounds like a bargain, a property with an AOC is still not likely to be all that cheap and as a buyer without any agricultural links, you should tread carefully.