I won’t claim to have the definitive answer, but one recurring theme in the poem is the morning sun as the source of the soul and of divine inspiration. Aurora is even called out within the poem as a name that means the dawn. Some instances of it include Aurora opening the window and her soul to the morning sun, Marian having been born to humble origins, but facing the east and inspired by some spirit, and Aurora’s suitor calling her a “Chaldean” who loves her “Eastern” books (meaning ancient Greek; Chaldea is now part of modern Turkey). There are some other references to the east in the poem, like her saying that her aunt who wants her to say yes to his proposal is blowing a wind from the east, and perhaps to the garden east of Eden.
In context, the previous stanza is talking about something like Plato’s conception of the soul (to which there are many allusions in the poem) and the next is talking about aspiring to be closer to God. So the metaphor is, at least in part, about humans as coming from the east and wandering, like beasts, to the west in search of food and comfort. while our higher selves aspire to return.