"Hope" is the thing with feathers -
That perches in the soul -
Dickinson opens the poem by introducing the extended metaphor that is the subject of this poem. She refers to hope as "the thing with feathers," an image that is developed and illustrated through the rest of the text. it sets up the idea of hope, in the reader's mind, as something persistent but not invincible.
And sings the tune without the words -
And never stops - at all -
Dickinson develops the image of the bird she introduced in the first two lines. She frames its melody as one that does not end, regardless of circumstance. She foreshadows the bird's potential for endurance, and leads the reader to expect that it will be tested.
Yet - never - in Extremity,
It asked a crumb - of me.
Here, Dickinson is suggesting that hope does not require anything from humans. She uses the image of the bird not asking for crumbs to illustrate this. The bird's song is given selflessly, in much the same way that hope does not hinge on certainty or clear expectation.