A decidable language is a type of formal language for which there exists an algorithm that can determine whether any given string belongs to that language. This means that for every possible input, the algorithm will eventually provide a yes or no answer, indicating membership in the language. Decidable languages are important in theory of computation and automata theory. Examples of decidable languages include regular languages and context-free languages. These languages can be recognized by specific computational models, such as finite automata or pushdown automata. In contrast, some languages are undecidable, meaning no algorithm can determine membership for all possible strings.