He clasps the crag with crooked hands; (line 1)
The speaker must have a reason for imagining the eagle to be a male. We think he embodies an old-fashioned masculine ideal. The eagle is a type of explorer, and until recently, great explorers were generally thought of as men. The eagle is ruggedly independent and perseveres with the help of his "crooked hands."
in lonely lands (line 2)
Tennyson was a sucker for romantic explorer types. In one his most famous poems, he rewrites the Greek myth about how the Greek sailor Ulysses led his crew into danger. In Tennyson's version, Ulysses is a bold and daring adventurer. In this poem, the eagle doesn't mind spending its whole life in solitude, as if it were a character in a John Wayne western. We're thinking, "Of course not, he's an eagle!"
Ring'd with the azure world, he stands (line 3)
The eagle is idealized as the center of the world, surrounded by a blue halo. Every guy's dream, right? We're only half-joking.