Parity refers to a simple check of the number of bits that are 1. If the parity information is stored (or transmitted) along with the data it is possible to detect errors. For instance in a system using even parity there must be an even number of 1's. Thus, if your data is 00110100, the parity would be 1. (There are 3 ones in the data and 1 in the parity for a total of 4.) If this information was transmitted and the recieving end got 00111100 with a parity bit of 1, it would be able to tell that there was an error in the communication. (It can't tell where the error is so it would have to retransmit the entire stream.)
Note: While it is possible to detect an error in most cases, if there is an even number of errors then it isn't possible to detect an error with simple parity.