The speaker looks at the small rivulet which he knows well but won't be seeing in the future (the poem is usually taken to mean that he is thinking about his own death.) He contrasts his own future absence or non-being ("Not by thee my steps shall be") with the way the rivulet will go on its natural and eternal course, growing into a river and flowing into the sea. The river could be seen as life itself, endlessly continuing, while individual lives fade away (as the rivulet fades into the larger river.) The poet seems to find this idea both comforting and sad.
You could compare this poem with others Tennyson wrote about death such as "Crossing the Bar."
You could compare this poem with others Tennyson wrote about death such as "Crossing the Bar."
