Any mistaken belief other than a mistake of law. Examples include erroneous beliefs about the meaning of some term or about the identity of some person.
In criminal law, a mistake of fact can usually operate as a defense so long as it is reasonable. With crimes that require specific intent, even an unreasonable mistake of fact might work as a defense.
In contract law, a mistake of fact may be grounds for rescinding or modifying a contract. A party that interprets a term one way, but has reason to know that another interprets it differently, should bring the issue to light before the contract is closed. Failure to do this often pushes courts to construe the meaning of the term against the party which had knowledge of the possible mistake.
For more on mistake of fact, see this George Mason University Law Review article, this Law and Philosophy Journal article, and this DePaul Law Review article.