In a request for quote, the participants asked respond with quotes, and the requester looks at them and decides whether to trade and with whom. In the CFTC definition, the requester sends a request for a quote to buy or sell a specific instrument to no fewer than three participants in the trading system, all of whom may respond. The three must not be affiliates of or controlled by the requester or each other1.
Consider a hypothetical example in which N Corp. asks three dealers for the fixed rate on an interest rate swap. If they come back with 1.50%, 1.52%, and 1.55%, in a trade where N Corp. pays the fixed rate, 1.50% is the quote with the lowest interest to pay.
A request for quote differs from an order book, where every participant can enter multiple bids and offers, see the bids and offers of others, and transact on them2. On a US swap execution facility, a swap subject to the trade execution requirement (other than a block trade) that is executed by request for quote must also be offered together with an order book3.