In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole.
Suppose that Lois Lane believes that Clark Kent will investigate a news story with her.
Thus, the sentence "Lois Lane believes that Clark Kent will investigate a news story with her" is true.
However, the statement, "Lois Lane believes that Superman will investigate a news story with her," is false.
Lois Lane doesn't believe that Superman is Clark Kent and the propositional attitude "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.