Coots are small water birds with large webbed feet. A brook would therefore be its natural habitat. Unfortunately for coots, they're also quite popular birds to hunt. In "The Brook" Tennyson uses the expression "herns" to describe hunters. This is an old English word whose use here emphasizes the great age of the brook. As the speaker—the brook, no less—says on a number of occasions in the poem:

For men may come and men may go,
But I go on for ever.

One gets the impression that this is a place where hunters have been coming for centuries to hunt coots. But the brook itself has been around for much longer than either man or animal. It flows down the hill as it's always done—stealing by lawns and grassy plots—and slipping and sliding among the skimming swallows (another form of bird life which has haunted the brook since time immemorial).