What it means
Means catching someone bang in the middle of doing the thing, with the proof still practically stuck to them, so any excuse sounds flimsy straight away. You use it for those gotcha moments when someone's been nicking, sneaking, cheating or blagging, and they've been spotted before they can wipe the crumbs off and act innocent.
Usage examples
"Mum barged in and caught my brother red-handed, spooning the birthday cake. He blamed the dog, but he had icing on his eyebrows, absolute melt."
"The shopkeeper caught the teenagers red-handed swapping the price labels on the trainers, called their mums on speakerphone and made them re-stick everything before letting them go."
"I caught my husband red-handed eating the last of the kids Easter eggs in the kitchen at midnight, chocolate on his fingers, foil on the floor, denied everything anyway."
"He got caught red-handed trying to sneak his own snacks into the cinema, crisps poking out his hoodie pocket and all."
"Don't even chat to me about innocence, you were caught red-handed in the group chat sending my selfie to your mate."
Where it comes from
This one really does come from old Scots law. Red-hand meant someone was seized with blood still on them after a killing or while poaching, so the guilt was right there in plain sight. Writers like Walter Scott helped it spread into wider English, and later it loosened up into everyday talk for getting blatantly busted.