I don’t know where the name comes from. A machinist might call it cutting oil. It helps disperse the diamond, lubricates, and helps swarf removal. Diamond is traditionally used with a light oil. Many people use WD-40, but I’ve heard of trombone oil, silicone/teflon grease, or even nut oils being used.
There are ways to make diamond water-friendly, as in the Gearloose water-based Diastiks. They work fine with just water, though you can use a fluid which helps the lap stay damp, and actually absorbs water from the air.