In "Our Casuarina Tree," the first line uses zoomorphism, describing the vine in animal terms (as a python). This is used to illustrate movement, making the tree seem more actively alive and also, by implying movement, there is a subtle indication of the process of time.
The line "the giant wears the scarf" is a personification of the tree. For the speaker, the tree is a link to her past. In a way, she treats the tree like a person that can "tell" (conjure) these memories as if it (the tree) could speak and tell these stories.
In the last line of the second stanza, the speaker uses a simile to describe the water-lillies "like snow enmassed."
In the third stanza, the tree is personified again singing its "lament" which might be the wind rustling through the leaves, a "dirge-like murmur" mourning the loss of the past.
Personification is used again in the next stanza. Examples are the "eye of faith," "the waves gently kissed," and "the earth lay tranced in a dreamless swoon." The speaker envisions nature (the tree, waves, the earth) as a living and maybe even a conscious entity recalling (dreaming) links to the past.
Again the speaker personifies the tree, hoping, in the final stanza, that the tree will be remembered like other favored trees, just as she remembers the people in her life. She mentions Borrowdale and this is a reference to Wordsworth ode "Yew-Trees" another poem praising trees. "Fear, trembling hope, and Death, the skeleton, and Time, the shadow;" is from Wordsworth's poem.
The Casuarina Tree is a symbol for life and memory. Since trees tend to live much longer than humans, they are used in poetry as living connections between generations of people.