A PROM leaves the factory blank, with every connection in place. The user programs it once with a device programmer, which sends pulses that blow tiny fuses wherever a bit should change. A blown fuse can't be repaired, so programming is one-time: such parts are often called OTP (one-time programmable).
Compared with a mask ROM, a PROM lets small companies and prototypes set their own contents without paying for a custom mask. Compared with later types, it can't be corrected: a mistake means throwing the chip away.
Like every ROM, it's non-volatile.
Memory aid for the family: each extra letter adds a freedom.