Jawf is an inner cavity or hollow, and al-ʿayr can denote a donkey. The phrase ka-jawfi al-ʿayr emphasizes a valley that appears hollow, empty, or forlorn. More than one detailed reading of this comparison is possible; their shared core is desolation and emptiness.
Grammatically, wa-wādin introduces the place; ka-jawfi al-ʿayr supplies the simile; qafrin its desolate quality; and qaṭaʿtuhu the speaker's act of crossing it. Place, character, and action therefore emerge in sequence.
The word qafr is more than topographical information: it supplies the silent setting in which the wolf's howling in the second hemistich becomes especially striking.