The speaker does something strange: they "put away" their own head, as if it were an object to be stored on a shelf. The head is called a "friend to this arson," which suggests the mind has been setting fires, perhaps through racing thoughts, anxiety, or some kind of inner torment. The speaker admits, almost in passing, "for I am ill," and that small aside explains the whole act. Rest means getting away from the thing that keeps burning.
What follows is quiet. The speaker simply walks "to see how things are / in his absence." Calling the head "his" makes it feel like a separate person, someone who has been left behind. The mood is calm but a little eerie, a mix of relief and curiosity. There is something gentle in the idea of checking on the world while the troubled mind is out of the picture, though the poem leaves open whether that peace can last.