This term was coined on the website, Fanpop. A user had meant to say "opinion" but typed onion instead in a question posted. This started a chain reaction of jokes about respecting the onion, pissing the user off!
Use this term whenever the word opinion comes into a discussion. It will succeed at both confusing and angering the person you say it to. It also helps if you shout it repeatedly.
Person A: I hate the color pink!
Person B: STFU!! Pink is awesome!
Person A: Hey! Respect my opinon!
Person B: F*ck your onion!
Person A: HEY! "Respect the onion."