By personifying both the lost aspens and the countryside at large, the speaker suggests that the natural world is a living thing: conscious, loving, and all too easily destroyed.
The speaker remembers the fallen aspens as affectionate protectors. Holding up the "airy cages" of their branches, they "quelled or quenched" the sunbeams in leaves, creating a shady haven that "dandled" the people who walked below—that is, that gently rocked or bounced them. The image of the trees cradling and rocking the speaker's "sandalled" shadow evokes branch-shadows swaying in a light wind at the same time as it paints a picture of a loving parent cradling a baby. To be under the aspens' gentle shade was to feel cared for, the speaker remembers.
Of course, that's all over now: the aspens are gone. The speaker laments not just those trees, but the countryside in general, which people are all too apt to thoughtlessly destroy. "Country," he says:
[...] is so tender
To touch, her being só slender,
[...]
Where we, even where we mean
To mend her we end her,
Here, the whole countryside is a living woman, a goddess who contains many little goddesses. The personified trees were part of the bigger life of a personified world. The speaker's vision of nature starts to feel fractal: every little part of the living world is itself a living world. Kill any one tree, and you break the pattern, "end[ing]" the life of the whole countryside.
Through personification, then, the speaker insists that the natural world is one big kindly, living, beautiful being—a caring parent that humanity callously mistreats.