He clasps the crag (line 1)
A "crag" just sounds like a place you wouldn't reach easily, doesn't it? Maybe if you had amazing rock-climbing skills, but even then, it would be disheartening to see the eagle flap its wings a few times and perch on the ledge above you. The eagle explores the upper reaches of the earth.
Close to the sun in lonely lands (line 2)
The eagle is so far above the earth he has almost left the atmosphere. Obviously, the speaker is exaggerating here. The phrase "lonely lands" continues the theme that the crag might as well be Antarctica for all the people who have been there.
Ring'd with the azure world (line 3)
The sea and sky are "azure," and these are both places where humans can't live. To us, they are a different "world." The rich blue color of the sky makes the air sound firm and substantial, like you could swim in it.