What does the poet mean by "the azure world" in the text of "The Eagle"?

In line 3, when the narrator describes the eagle as "ring'd with the azure world," he means that the eagle is surrounded with or encircled by the bluest of blue skies: azure is the name of this pristine sky blue color, the blue we see on a perfectly sunny and clear day.  The eagle is perched very high up in the air, "clasp[ing] a crag" that is "close to the sun" (lines 1, 2).  He is alone and holding on to a tall mountaintop.  Thus, it seems as though we are sort of seeing the world the way the eagle sees it from high up on his mountain perch: the eagle perceives himself as being at the center of this blue circle of sky around him, and so this is what we see from the description as well.