Anyone who has lain awake all night will recognize the situation here. The speaker can't sleep, and instead of resting, his mind races. He imagines this as a contest between himself and a crow, and the crow wins easily. It finishes first and goes off to play, while the speaker is left behind, still awake and still turning things over.
The crow seems to stand for a quick, wild, untroubled kind of thinking, one that moves freely and doesn't get stuck. The speaker's own mind feels busier and stranger by comparison. He calls it a "busy dance" and then "a great stranger," which is a surprising thing to say about your own head. The last line, "I am loath to settle in it," suggests he doesn't want to make himself at home there, or can't.
The mood is tired but curious, even a little amused. There's unease in the sleeplessness, yet the speaker watches his restless mind with wonder as much as frustration.