The eagle is the active figure in the poem and seems to possess the power of choice in addition to an implied power to destroy. In these ways, the eagle may be said to be presented as a symbol of power in the poem.
The second stanza depicts the eagle as "He watches from his mountain walls." This vantage point is suggestive of a power of choice. The eagle can remain removed or distanced from the world that he watches. He is literally above it and figuratively above it too, to some extent.
In commanding the view, as it were, the eagle can be described as a commanding figure.
Also, since power is relative, we can note that there is nothing and no one else in the landscape that might influence or dictate the eagle's behavior. The eagle is a figure of self-possession and independence, alone to make its choices for itself. Power over one's self is one aspect of command, control and power.
The eagle is also described as being "like a thunderbolt" when he falls. This image aligns the eagle with nature but also with a traditional emblem of power. Zeus, the Greek god, was known to use thunderbolts as a weapon. The subtle correlation in the poem aligning the eagle with this chief Greek god also connects the eagle to the idea of power and superiority.
As a god, Zeus was unmovable. He was the chief power in the Greek world. If the eagle is somehow affiliated with Zeus, the eagle is also then affiliated with notions of power.
By associating the eagle with nature, the poem also suggests that the eagle may be a symbol of nature's power. As a symbol of nature, the eagle is not just a powerful figure in itself but becomes a representative of the enduring and far-reaching power of the natural world.
"...this association makes the eagle seem, like the sun, more powerful than anything of this earth" (eNotes).
While reading the eagle as a symbol of power in these ways is certainly a defensible way to interpret the poem's meaning, others have suggested that the poem deals instead with age, aging and human death. The details of wrinkles and crags and a final fall are used to support such a reading.