The Holy Therns are a species who don't show up until later in the series. They are revered as essentially gods to the red and green men of Barsoom. Their skins is white and they have blonde hair (which for some reason I remember being a wig).
One would best compare them to the Gods of Olympus as they lived in a place where the red and green men believed to be holy and where you would go to die. It's basically a forest and mountain far off from where the red and green men typically inhabit.
Carter and Tars Tarkas encounters them in the second and third books of the series where they learn that the horrible truth about the Therns in that they merely trap those who come into their land to die as slaves and that they essentially control the great white apes.
Their teleportation, in the books at least, is revealed to be a trick of shadows, hidden passages and I believe mirrors.
The immortality is a superstition tied to their being seen as supernatural. Of course, Carter and Tars Tarkas quickly learn that they can be killed just as anyone else and that the only real difference between the Therns and the red/green men - and later the black men - is skin color.