The Deep Darkness was either a void, a pocket universe or some kind of dimension that existed outside Normal Space. During the Dark Times of the universe, the Eternals banished the witch-like Carrionites and the Hervoken to the Deep Darkness.
Three Carrionites escaped from the void and in 1599 opened a gateway between Earth and the Deep Darkness. All trapped Carrionites began to enter Earth but the gateway was closed by the brilliant words of William Shakespeare. (TV: The Shakespeare Code)