At the most basic level, non volatile memory stores data without power. Two examples of devices that use non volatile memory are hard drives and CMOS chips (the chip that holds your BIOS information).
Non-volatile memory is important for long term storage of essential system information and data. Just imagine how much trouble it would be if you had to reenter everything contained on your hard drive. Not so fun, huh?
EPROM (erasable programmable read only memory) is another form of non-volatile memory. There are a few varieties of this type including:
flash EPROM (which erases and replaces the data all at once, as opposed to one byte at a time)
EEPROM (electronically erasable programmable read only memory)
OTP (one time programmable) EPROM. Many pieces of hardware use these chips to upgrade their firmware (software contained on the hardware).
CDs and DVDs are also a form of non-volatile memory, storing their data in pits on the surface of the disks. They use optical technology as opposed to most other types of computer storage, which are typically magnetic based. This makes them exempt to certain problems faced by other forms of media (such as data loss caused by proximity to magnets). Optical disks, however, have their own set of problems including scratching.
There are a few advantages to products using nonvolatile memory. They are typically less costly to produce than volatile memory (such as RAM), data can be stored up to ten years (sometimes longer) without a power source, and it allows hardware to become upgradeable. This allows developers to both adjust to new technologies, and helps to stave off complete hardware upgrades.
While nonvolatile memory is not always the best choice — could you imagine a computer trying to use nonvolatile ram? - it is well suited for a number of situations