The contrapositive of a conditional statement is formed by negating both the hypothesis and the conclusion, and then reversing their order. For example, if the original statement is "If A, then B," the contrapositive would be "If not B, then not A." Both statements are logically equivalent, meaning they will always have the same truth value. Understanding the contrapositive is important in logic and mathematics, as it helps in proving the validity of statements. By demonstrating that the contrapositive is true, one can conclude that the original statement is also true, making it a powerful tool in logical reasoning.