Often used as an answer to o rly. It is synonymous with an owl sporting a monocle and a pipe. Other answers to o rly are ya rly and cho rly.
Meant to sound sophisticated, which is an oxymoron based upon its origin.
James: Dude, Pamela Anderson is a total babe!
Chris: o rly?
James: ya rly.
Chris: Quite Rly.
James: Indeed, good friend.