Condition

patt /; test is a pattern which matches only if the evaluation of test yields True.

lhs :> rhs /; test represents a rule which applies only if the evaluation of test yields True.

lhs := rhs /; test is a definition to be used only if test yields True.

Examples

Pattern matching with a condition:

Cases[{1, -2, 3, -4, 5}, x_ /; x > 0]
(* {1, 3, 5} *)

Conditional replacement rule:

{1, -2, 3, -4} /. x_ :> x^2 /; x < 0
(* {1, 4, 3, 16} *)

Please visit the official Wolfram Language Reference for more details.