The Apokoliptians refers to anything from the planet Apokolips, particularly New Gods that inhabit the planet Apokolips. Like their brothers from New Genesis, they are members of the same species, as they both originally were born out of the destruction of Urgrund, which caused them to be separated when the world was split into two separate planets: New Genesis and Apokolips. The Apokoliptians were incredibly ruthless, and the conditions on the planet were considered dreadful, as the lower class citizens, known as the Lowlies, were made to be slaves. But this was a position that many of them found to be desirable, even though they were in dreadful living conditions.
Darkseid is the ruler of the Apokoliptians. He rules over the rest of his subjects and even though its' terrible, his subjects are proud to be slaves of him. This is especially odd considering how terribly they are treated, especially the Lowlies.