From CS2800 wiki

A language is another name for a set of strings (i.e. a subset of [math]\href{/cs2800/wiki/index.php?title=%5CSigma%5E*&action=edit&redlink=1}{\Sigma^*} [/math]. In the context of automata theory, languages can be thought of as "problems" or "specifications". The "problem" is "solved" by an automaton that accepts all elements of the language and rejects everything that isn't in the language.