1. The little girl’s mother caught her red-handed trying to steal cookies from the cookie jar.
2. The two men dropped the stolen goods when they heard the police car sirens. They didn’t want to get caught red-handed.

Dating from the 15th century, this idiom is a reference to the notion of killers being caught with the blood of their victims on their hands. The meaning later expanded to being caught in the act of any kind of wrongdoing.