A summary of Tennyson's "The Brook" is a very straightforward thing once you realize that the poetic voice, or the speaker, in this simple allegorical poem is the personified brook (who may be viewed as Immortality in opposition to humankind's toil and transience): "I come from haunts of coot and hern,". [A haunt is a much frequented place. A coot is an aquatic bird. A hern is a heron bird.] The brook is saying that it originates at a large body of water where coot and hern congregate.
Each stanza highlights the brook's progress to its destination that is revealed in the last stanza, which is "the brimming river," and to the delivery of the theme and purpose of the poem, which is that "men may come and men may go, / But I go on forever."
The brook's journey takes it past (S. 2) "a little town" where people dwell; by (S. 3) "Philip's farm" where a family grows; (S. 4) over stones, eddies and pebbles; and (S. 5) past curves and willow-weed, while (S. 7) it chatters and flows and "men may come and men may go."
It (S. 8) winds about with blossom and trout above (S. 9) "golden gravel" and (S. 10) draws them all along, for it (S. 11) goes on "forever." It passes (S. 12) lawns, forget-me-not flowers and "happy lovers" as it (S. 13) slips and slides with swallow birds and sunbeams. Under (S. 14) "moon and stars" it (S. 15) curves and flows