There is always the possibility of a bit in memory being incorrect. In fact, it is a reality, even with enormous odds against it - your system has millions of bits being reset almost constantly. The electronics of this setup implies that error will occur. Undoubtably, your machine has had erroneous bits and you have been completely unaware. In cheap/faulty RAM, this can cause errors in the system's operation. Single bits may pass, but double bit errors often cause operational problems.
The reason you might have ECC is twofold:
1) Your system is in high use and time, stability, and correct results are important. For example, if you are performing complex, maybe highly recursive, operations, or the server is processing financial transactions, or is simply a major multiuser system.
2) Your system is subject to regularly high ambient temperatures (possibly in close proximity to other machines or simply a large, hot-running machine). Thermal conditions will increase, even exponentially, the problem.
Parity RAM traditionally has an extra bit for every 8. This 9th (parity) bit is calculated and set at write, then recalculated and compared at read (basically). A discrepancy in the bit calculation flags corruption. You have a 1/9 chance that the error did not occur in the parity bit.
ECC RAM (a modern form of parity) usually has a handful of parity bits for every 32 or 64 bits. Single bit errors, by far the most common, are corrected automatically. Two bit errors are only flagged, not corrected. These can still possibly cause system crashes, but are dropped by the CPU memory subsystem (not all programs are ready for somethings to fail).
