The message of "The Eagle" is that being in a position of power, especially a position of absolute power, can be extremely lonely and even dangerous. The eagle itself is a symbol of a person in such a position, personified as possessing "crooked hands," which seems to imply that the figurative leader rose to his position of power through some corrupt means (as "crooked" can mean bent or corrupt). The adjective "crooked" also bears connotations of age, suggesting that the figurative ruler is older. The eagle is "Close to the sun," literally quite high up on a mountain; the leader is figuratively elevated, possessing more power than anyone else over whom he rules. He oversees "lonely lands"; indeed, it is a lonely position for both eagle and leader, because the position requires solitude. One cannot rule absolutely if power is shared.
The "wrinkled sea" literally exists far below the eagle's perch, and it also signifies the "crawl[ing]" and powerless subjects of the leader's power and position. Moreover, "wrinkled," like "crooked," underscores the connotations of agedness. The "mountain walls" literally refers to the mountain on which the eagle "stands" and figuratively evokes the stone keep or castle from which the leader surveys his dominion. "He watches" from this literal and figurative heigh. The eagle dives "like a thunderbolt" to catch his prey, mercilessly and without hesitation, and the leader might do something similar, enacting his justice "like a thunderbolt"—that is, doing so inexorably and with great authority. The word "falls," however, also provides a clue as to his undoing, as most leaders do not simply hand over their power to their successor. Instead, they are often overthrown, ousted from their position by someone even more powerful, and such a "fall" from power can be precipitous indeed.