The eagle holds on to a cliff with claws that look like "crooked" or deformed human hands.
He "clasps" the cliff the way you clasp someone's hand in a handshake. The eagle is holding on super-tight to the rock.
He's also a male eagle. Don't ask us how the speaker knows this. If you were being critical of Tennyson, you might say that the eagle is supposed to make us think of so-called "masculine" virtues like strength and self-sufficiency.
We all know that a "crag" implies sharp rocks and cliffs, but we can get more specific than that. A crag is not just a cliff, but it's the part of a cliff that juts out from the main body of rock. Crags can be massive – almost the size of mountains themselves – but they always jut out from some larger rock. They are exposed and hard or dangerous for humans to access. The eagle is out of our reach.
As if to emphasize the eagle's inaccessibility, the first line features alliteration using the harsh, hard "c" sound.
The eagle is thinking, "Whose hands are you calling crooked, Poet?" The comparison of the eagle's claws to hands means that the poet is not trying to describe nature independently of humans. He describes nature in reference to humans.
Close to the sun in lonely lands,
The eagle is really high up there, and all by himself. So far up that it appears to be near the same height as the sun. (What's that, like 93 million miles or something?) OK, "close" is a relative term. If the earth and the sun are the two opposite poles of distance, than the eagle seems closer to the sun than to earth, which makes us wonder how the speaker can see the eagle so well, if it's so far away.
"Lonely lands" is another straightforward example of alliteration. It's also an unusual way to describe a high rock surrounded by sky.
Why does the poet use the plural, "lands," if the rock is the only land in sight? Once again, the eagle's world is described in reference to our own earthly world, where we have lands in abundance. And do eagles get lonely? We'd guess not. Otherwise they'd likely hang out with each other more often.
Ring'd with the azure world, he stands.
The eagle is surrounded by blue skies. The blue sky forms a "ring" or circle around the eagle.
We now appear to be seeing the world from the eagle's perspective. The eagle sees nothing but blue, but the person looking at the eagle would also see the rock on which it was perched. The speaker's imagination has leapt into the sky to join the bird.
"Azure" is a kind of deep, bright, beautiful blue color often associated with clean ocean water. When the sun is shining, the sea appears azure, and so does the sky. The sky also appears more blue, or azure, the further away from the horizon that you look (source). Basically, the eagle is at the very center of the bluest, most central part of the sky. It's in the center of the center.
Tennyson contracts "ringed" to "ring'd" to emphasize that we should pronounce it as one syllable, and not as "ring-éd," as it often is in Shakespeare and other Renaissance plays.
Speaking of pronunciation, "azure" is an incredibly difficult word to pronounce. If you know any French, you can just say, "azeure." The rest of us can take comfort in the fact that even the people on this cool pronunciation website can't seem to agree.
For all the fuss that the poem makes about the eagle, you'd think it were doing something really interesting, right? False. The first stanza builds to the thundering climax: "he stands."
Let's review: we first met the eagle when it was clasping the rock in order to stay upright and now it's, um, still…just…standing there. However, we can note that "stand" sounds like another projection of human qualities on to the bird. Not that birds don't stand, but when they are perched, don't we normally just say "perches"?