Innocence
The overarching theme in this text is that of innocence. In the very opening lines, the poet sets the precursor to this theme, and establishes that the object of his poetry is the "youngest virgin-daughter of the skies". By this line, it can be inferred that the poet attempts to say that Anne is the paragon of innocence. The lines that follow reiterate this sentiment.
Another thing that further exemplifies this idea is the fact that Anne had died young, with her innocence intact. He also says, "Her wit was more than man, her innocence a child!", and implies that while she was brilliant in her own right, her innocence was indisputable.
Nature
The visual imagery in the poem contributes to the theme of nature. From the very beginning, nature imagery is used in the poem. Extensive mention of natural elements further adds to this theme. Anne Killigrew is compared to different elements in nature, and these elements add to the regal tone of the poem.
Death
This poem can be read as an elegy in honor of the eponymous heroine of the poem, and hence another significant theme is that of death. There is a certain connection between the innocence of Anne Killigrew with her untimely death.
It is made clear that she has passed away, having been welcomed by the heaven. The nature imagery also adds to this theme as the "immortal green" has been mentioned, perhaps to imply that while she is dead, she has been immortalized in her art.