As with many aspects of his fictional world, C. S. Lewis leaves the origin and nature of the Dark Island encountered in of the Dawn Treader Voyage of the Dawn Treader unexplained. This fan-based article will attempt to describe both to curious readers.
Tash's first entry into the world of Narnia, along with his minions, was on a sizeable island in the Eastern Ocean. Tash's Servants made this island their fortress, a stronghold from which to subdue the rest of that world. The evil permeated the very soil of that land, dissolving it and turning the island into nothing but a mass of blackness, stench and evil, a copy of Tash's Country.
With the defeat of the White Witch by the Pevensie children, the demons of Tash that had aided her in her conquest of Narnia lost their horrendous powers, and were reduced to nothing more than black shades, bound to the island which had been their home for so many centuries. But one power remained with them: Their ability to play upon the desires...and fears...of mortals. Like the Sirens of Homer's Illiad, they lured seafarers to their dungeon by twisting their desires for pleasure, and then tormenting them once they had entered by manifesting themselves as the mens' most terrible nightmares. Worse still, once a mortal entered this blackness, there was no way out, save by the help of Aslan.
The original island had been a normal land mass, similar to any other island in that ocean. However, with the corruption of Tash the island sank into the blackness and evil of the demon's power. The darkness of which it was composed ever afterwards was a representation of the heart of Tash: Evil and horror personified.
In The Last Battle, the characters got a final taste of the island's darkness when they saw Tash gliding past the tower in which Tirian, Jill, Eustace and Jewel were residing. A cold fear washed over them, although much less in intensity than the fear felt on the Dark Island. The smoke of which Tash was composed was the same of the Dark Island, and the effects were similar. However, the power was significantly lessened with the overthrow of the White Witch in Narnia.
The powers on the Island proved to be no match for the power of Aslan; when he rescued the crew of the Dawn Treader from the nightmares which plagued them, his light vaporized the nigh-solid smoke, causing it to gradually disperse as a dark mist. Sailors coming through that area would still feel a tingle of icy fear...but the terrible power the demons had wielded was gone from that world forever.