The if and only if symbol is used as a logical statement in math. Typically the symbol is used in an expression like:
$A⟺B$
In plain language, this means that if $A$ is true, then $B$ must be true and if $A$ is false, then $B$ must be false.
Symbol  Format  Data 

⟺  Unicode 

$⟺$  TeX 

SVG 