Tash's Country is the place where all species are sent to if they reject Aslan by committing evil acts in life. It is presumably a place of unimaginable torment and suffering, ruled by Tash. It is plausible that those who fail Aslan's judgement are sent here to be condemned for eternity.
Note[]
It should be noted that C.S. Lewis clearly depicted Tash's Country to be the Narnian version of Hell. The polar opposite of Heaven is Hell, and C.S. Lewis clearly states that the opposite of Aslan's Country is Tash's Country.
It's possible that Tash's Country is a cruder and uglier representation of the living Narnia, since Aslan's Country is the more realistic and life like version of the material world.