It was given this name by American paleontologist Roy Chapman Andrews, who visited in the 1920s. The area is most famous for yielding the first discovery of dinosaur eggs. Other finds in the area include specimens of Velociraptor, and eutherian mammals.
The red or orange color of the sandstone cliffs (especially at a sunset), hence the nickname.
Not all parts of the world had substantially different climates 85 million years ago than they do today, but Mongolia's Gobi Desert seems to have been as hot, dry and brutal as it's always been. We know this from the fact that so many of the dinosaur fossils unearthed at the Flaming Cliffs formation appear to have been buried in sudden sandstorms, and that very few large dinosaurs (which would have needed equally large amounts of vegetation to survive) lived here.
This site is also close to the region where researchers unearthed the tangled remains of a Protoceratops and a Velociraptor, which appear to have been locked in a death struggle at the time of their sudden demise.When dinosaurs died at Flaming Cliffs, they died quickly: burial by fierce sandstorms is the only way to account for the discovery of this dinosaur pair (as well as numerous, articulated Protoceratops skeletons found standing in the upright position).