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 hatred of streams and will spend the rest of your days trying to avoid them.