A logical operator denoting logical equivalence or "if and only if" in mathematical proofs and logical statements.
Examples
Logical equivalence
A \Leftrightarrow B \text{ means 'A if and only if B'}
Mathematical definition
x \text{ is even} \Leftrightarrow x = 2k \text{ for some } k \in \mathbb{Z}
Set equality definition
A = B \Leftrightarrow (x \in A \Leftrightarrow x \in B)