In computer processors the parity flag indicates if the numbers of set bits is odd or even in the binary representation of the result of the last operation.
If the result of the last operation were 26 (11010 in binary), the parity flag would be 0 since the number of set bits is odd.
Some microcontrollers, notably the ubiquitous 8051, include a parity flag to help with implementing RS-232 and other serial communication protocols, in lieu of a UART with parity support.
x86 processors include a parity flag because they are descended (via the Intel 8086, 8080 and 8008) from the Datapoint 2200 terminal, which was designed for serial communication duties.
[1] The C2 flag is set when e.g. incomparable floating point values (NaN or unsupported format) are compared with the FUCOM instructions.