He clasps the crag with crooked hands; (line 1)
The alliteration of words that begin with "cr" or "cl" mimics the sound of hard rocks. The landscape is unforgiving, and from the speaker's perspective, you'd have to have something twisted or "crooked" about you to live there. By calling the eagle's talons "hands," the speaker makes the eagle seem in some way human, although it perches on a cliff that people can't access.
Close to the sun in lonely lands, (line 2)
The sky is only "lonely" from a human perspective. The speaker admires the eagle's separation from the busy, social world below.
Ring'd with the azure world (line 3)
"Azure" stands for the sky and also the sea. We think the sun must be out, because "azure" is a bright blue and not at all hazy. The eagle is at the center of another, empty world. The ring of blue surrounds it like a religious halo.