Ray Palmer's A.T.O.M. suit is said to be made out of "dwarf star alloy". What exactly is this? Is it literally from a dwarf star? Or is it just a fancy name for something else?
Yes, it is from a dwarf star
Specifically, this is a reference to the character of the Atom from DC Comics, who created his size-changing suit out of material from a white dwarf star.
In the show, Palmer gets it from a mine:
Yep, I just sent the notarized transfer of ownership. Now listen, I want to get a jump on the mining operations immediately. Let me know as soon as the first of the dwarf star alloy is extracted.
In either case, the material is literally a piece of a white dwarf star, though in the Arrowverse it would seem to be further underground.
As an aside, a white dwarf star has a density of about 1,000,000,000 kilograms per cubic meter. Assuming that little piece of star Palmer is picking up is 0.1 meters in radius, it should have a mass of about 4,000,000 kilograms, or a weight of about 10 million pounds. Even for a field scientist, Palmer is surprisingly athletic.