PROM chips do not lose their data when power is removed but, unlike standard ROM chips, come without a program already installed.
The programs for the PROM chips can be 'burned' into them with a special piece of programming hardware. Once burned this way the contents are never lost but nor can they be altered.
PROM chips are commonly used where engaging a chip foundry to manufacture a custom ROM chip would be too expensive.
PROM is expensive and is used for low volume applications.