The term "cremains" is a corruption of the term "cremated remains." It has fallen out of favor with most of the death-care profession as sounding too casual or disrespectful. See cremation in the ICCFA Wiki for more definition of cremated remains.
Is it true that cremated remains can be turned into diamonds?
Yes, there are companies that have developed a method combining intensely high heat and extreme pressure to turn the cremated remains - which essentially are carbon, of which naturally-occurring diamonds are made - into diamonds. They can do the same with a lock of hair.