The idea is protective in origin: a place name that had come to mean something was being used by wine from elsewhere, and the law was asked to stop it. What began as an anti-fraud measure became the primary way European wine is classified.
What the rules typically fix
The boundary; which grape varieties may be planted; a maximum yield per hectare; a minimum ripeness or alcohol; and in many cases minimum ageing periods and permitted methods. The tighter the appellation, generally the more it specifies.
The systems a reader will meet
France's AOC (now AOP), Italy's DOC and DOCG, Spain's DO and DOCa, Portugal's DOC, all sitting under the EU's PDO and PGI framework. The United States uses AVAs, which is a real difference rather than a translation: an AVA defines a boundary and requires a proportion of fruit from it, but does not generally dictate grapes, yields or methods.
What it does not promise
Quality. An appellation guarantees origin and compliance — that the wine came from where it says and was made within the rules. A poor wine made to the rules is entitled to the name, and frequently gets it.