Someone is red-handed if it's obvious they're guilty of some wrongdoing, or are even in the midst of doing it. If you catch your brother with his hand literally in the cookie jar, you can say you caught him red-handed.
A fancier way to say red-handed is the Latin phrase in flagrante delicto, or "in blazing offense." Aside from this legal term, you can also say "caught in the act." Red-handed comes from legal terminology too — specifically, a Scottish legal term that was inspired by the grisly image of a murderer who's been caught with bloody hands.