Wikipedia has this to say, which agrees with my understanding.
The Last Dangerous Visions is an unpublished sequel to the science fiction short story anthologies Dangerous VisionsDangerous Visions and Again, Dangerous Visions, published in 1967 and 1972 respectively. Like the first two, it was scheduled to be edited by American author Harlan Ellison, with introductions provided by him.
The projected third collection was started but, controversially, has yet to be finished. It has become something of a legend in science fiction as the genre's most famous unpublished book. [bold emphasis mine]
The scuttlebutt among fans was that the project simply overwhelmed Ellison. The first two Dangerous Visions anthologies were very popular, and the were a great many writers who wanted to participate in the Last anthology. The number of quality submissions became too large for a single volume, and Ellison was supposedly unwilling to prune out works that he thought were of high quality. Since one of the unique features of the Dangerous Visions series was that each short story got a special introduction written by Ellison in his capacity as editor and critic, the workload became more than he could deal with, and he eventually shelved the project.
In the meantime, a fair number of the stories were eventually published elsewhere. (Another feature of the Dangerous Visions series was that it only featured completely new stories.) Authors* who wanted the work they had submitted to get printed withdrew their stories and submitted them elsewhere. Since that often meant that the best work was being withdrawn from the project, the motivation for Ellison to publish the remainder must have fallen each time this happened.
So the result is this will probably never be published. Ellison is deceased, and without his introductions for the stories, the project would not really be Last Dangerous Visions. Those authors who wanted their work to get published anyway have probably seen to it that those stories were printed elsewhere. Up until Ellison’s death, some of them might have still been holding out hope for the project (Brian Wilson of The Beach Boys finished the SMiLE album after a thirty-seven year delay, although the final result was disappointing), but that’s not possible.
*Or their literary executors, as plenty of the people who submitted stories are deceased. For example, one unpublished story by Cordwainer Smith, “Himself in Anachron,” was submitted to Last Dangerous Visions after the author’s death. It was eventually published when Smith’s short stories and novellas were all finally collected in The Rediscovery of Mankind.