Latin is the language that Roman demigods at Camp Jupiter speak the most, and other than English. (The campers come from all over the world, so they can speak varied languages depending on where from.) Greek demigods are trained to read it, but they understand Ancient Greek better; Roman demigods can't interpret Ancient Greek as well.
It's said that Ancient Rome also spoke Latin, even though now there are none that speak Latin fully. It is what humans call a 'dead language'.
Often they would say the phrase, "Senatus Populusque Romanus" which for short is SPQR. The translation is "The Senate and People of Rome".