A brook is a small stream. On a hot day, you might enjoy wading in a babbling brook. As a verb, brook is a rather stuffy word for "put up with." The lord of the manor might say, "I will brook no trespassing on my land."
Brook is tailor-made for talking about what you won't stand for—it's always "brook no..." If you brook no criticism of your friend, it means you won't let people speak ill of her. If you brook no brooks, it means you've developed a bizarre stream-hating fetish and will spend the rest of your days trying to stop their flow.