Even parity and odd parity both refer to asynchronous communication parity checking modes; even parity sets an extra bit to 1 if the data item already has an odd number of "1" bits or to 0 if the number of "1" bits is even, while odd parity checking does the same but leaves the number of "1" bits odd. Parity bits are used to detect errors in devices that store memory.
Here's an example of odd parity. The transmitted message 01000000 has only one "1" in it. Converting this to odd parity adds a zero, which yields 0 01000000. The total number of "1" digits in the message remains one, which is an odd number. If a message is 10101100, that message has four 1s in it, giving an even number. Turning it into odd parity adds a "1" at the start, yielding 1 10101100.
With even parity, the results would have been reversed. The first message (01000000) would have a "1" added, yielding 1 01000000. The second message (10101100) already has an even number of "1" bits, to the parity message would be 0 10101100.
Both receiver and sender must agree to use parity checking and whether to go with even or odd methodology.