This poem seems to be about the relationship that the speaker has with her God and the way that it is never failing and is as certain as the passing of the seasons and the coming of daylight each day. The use of purple occurs in the second stanza of this poem, and appears in the following context:
Old the Grace, but new the Subjects--
Old, indeed, the East,
Yet upon His Purple Programme
Every Dawn, is first.
The capital in "His Purple Programme" clearly indicates that this phrase relates to God, and his programme of creation and the way that the world is set to run. Normally, the colour purple is associated with divine rule and majesty, and is used in other poems by Dickinson to describe, for example, the colour of Christ's robes. The use here therefore picks up on this divine significance. Since God is by his very nature divine and worthy to be praised, his plan or "Programme" is therefore likewise divine and to be admired. The colour purple bestows upon this programme the same kind of dignity and praise that should be bestowed upon God himself.