What does the method known as parity do?

In RAM, parity is a type of built-in error-checking system.

After the 8 bits in a byte receive data, even parity works by adding to total number of 1s. If the number is odd, the parity bit is set to 1; if the number is even, the parity bit is set to 0. When the data is read back, the total is added up again and compared to the first total. If the parity bit is 1, the data is error-free, but if the total is odd and the parity is 0, the chip recognizes a problem and gets rid of the data.

Odd parity works in the same fashion, just the other way around.