The above answer discusses the contextual factors surrounding this poem, and its likely connection to the physical place that was Amherst at the time of writing. Divorced from this biographical interpretation, however, it seems clear that the poem can be interpreted as a description of heaven, or some other unearthly place in which the "garden" is safe from the natural disturbances that would otherwise plague it, such as "frost" and "darkness." The idea of heaven, or God's kingdom, as "another country" is a relatively common one; Dickinson here uses imagery suggestive of the Garden of Eden as she describes the sky where is it always "fair" and there is always "sunshine," regardless of the darkness that may exist on earth ("there"—where the addressee, Austin, is.) The place described in the poem is one where leaves are always green, and the flowers "unfading." The invitation to "into my garden come," then, may represent an invitation to the recipient to join the speaker in her faith that such a place exists, beyond the boundaries of frosty, faded, earthly reality. 

Emily Dickinson wrote "There is another sky" in conjunction with a letter she sent to her brother, Austin. In the poem, she tries to convince Austin to return from Boston to Amherst. In this context, the poem is about place. Although Amherst is a place in the world, and therefore subject to change, Dickinson compares it to a heavenly place, one where things always remain the same. This is the idea that your home, or home town, might change but it will always be "home." Since that designation of "home" never changes, the place, in a sense, never changes. This is why she uses phrases such as "whose leaf is ever green" and "unfading flowers." 

There is a bit of ambiguity. Is Dickinson talking about heaven, Amherst, both, or something else. The last line is "Into my garden come!" This could easily be taken as a sexual (and therefore, incestuous) invitation (to her brother, Austin). However, given that the poem has hymn-like qualities, it seems more likely that this poem is about the nostalgic lure of Amherst ("home") and the everlasting promise of heaven. 

This conflation of worldly place and heaven has evidence in the poem. The first line is "There is another sky." The fact that "there" is used indicates an otherworldly place: something not "here." Later, in the poem, the speaker claims "Here is a brighter green." The "here" indicates a worldly place. The combination of "here" and "there" could imply a connection between the world and heaven. This theme is about the sense, or perception, of such places.