On one level, this poem could be read as an actual depiction of an eagle that employs some figurative language to achieve a more compelling and dramatic effect. On another level, this poem can be read as a commentary on supreme power and what it might be like to possess such power.
Our first clues are in line 1: "He clasps the crag with crooked hands." To clasp is to grip quite purposefully and forcefully and implies a strong desire to hold on to something, like one's power. Crooked, as well, has two definitions: bent, as an eagle's talon's would be, and corrupt, as someone who holds supreme power most likely is. Next, the area around the bird is described as "lonely lands," implying that the eagle has no one with whom he shares his place -- he, alone, has power; this is also the way supreme power works. In order to share the position, a supreme leader would also have to divide his authority, and supreme leaders tend to dislike giving away any of their power. This leads to a somewhat solitary existence. Next, the line "Ringed with the azure world, he stands," uses the word "stands" instead of "perches" as we might expect of a bird (line 3). If we think of the word "stands" in terms of someone taking a stand, or making their last stand, the word implies more than just being upright. It seems to signify some kind of powerful stance; perhaps the person who has supreme power is displaying that power or maybe he feels that it is threatened.
The next stanza begins with, "The wrinkled sea beneath him crawls" (4). One with supreme power has all the power, and so his subjects are powerless, and crawling is an action associated with powerlessness. Thus, the sea could be symbolic of the powerless masses over which the supreme leader rules. Until, finally, "He watches from his mountain walls, / And like a thunderbolt he falls" (5-6). This leader keeps watch over his country from atop high walls that both protect him as well as convey his power. The final line could signify a couple of different things: that when he strikes, this leader can do great damage; or that if this leader falls from power, it is a violent and quick process.