After the fall of Troy in ancient times, Aeneas, son of Venus led the Trojans into exile in Italy, founding a new civilization which later became the Roman Empire. Over time, their pantheon became much more disciplined, warlike and militaristic which the gods eventually adopted, producing demigods different from those conceived in their Greek aspects. There was a rivalry between the two groups which subsequently had many conflicts over the millenia.
Not much is known about this camp except that they fought the Greek Camp Half-Blood in a war that mirrored the mortals' American Civil War in 1864. Because of the toll this war took on their children, the gods decided to completely separate the Greek and Roman demigods to avoid further bloodshed. By weaving the Mist so thickly, the gods made the two rivals forget each other and would ensure it would remain so ever since.
Chiron, Lupa, and most likely others who also knew of this incident swore upon the River Styx never to speak of it. The Greek camp always knew there was a second camp on the west coast but had no idea that it was roman. Until it was revealed by Rick Riordan to both sides.
The Roman demigods are filed by their parents at the age of two years in a building known as the Wolf House where they are supported by Lupa, then if she judges them worthly she takes them to the Roman camp, like gladiators of Ancient Rome, where they are livestock marked with the symbol of their godly parent and the initial SPQR. Later, for each year spent at the training camp, they receive an additional line on their tattoos, like the Greek campers, who get an additional bead to their necklaces every year they spend at Camp Half-Blood.