There rolls the deep where grew the tree. O earth, what changes hast thou seen! There where the long street roars, hath been The stillness of the central sea.
The hills are shadows, and they flow From form to form, and nothing stands; They melt like mist, the solid lands, Like clouds they shape themselves and go.
But in my spirit will I dwell, And dream my dream, and hold it true; For tho' my lips may breathe adieu, I cannot think the thing farewell.
The images of nature here seem to suggest impermanence and flux where previously (in images of trees living a really, really long time) they suggested permanence.
This becomes pretty clear when he mentions the shadows "flow[ing] / From form to form" and the fact that "nothing stands." Mist and things melting also emphasize this image of flux and constant change in nature.
Tennyson is comparing this to the eternal nature of the spirit. While the earth is constantly in flux and nothing remains stable (even though we're talking about geological periods of time), the soul outlives even the earth.
Tennyson will always have a life in his spirit.
That's where real eternity comes in. So not even the old yew tree—which lives for thousands of years and tears apart skeletons and gravestones—can rival this kind of eternity.