A very
simple form of
error detection. An extra
bit is tacked
on (per
word, per
octet, per
message, whatever) to make the
total number of 1s
even (or
odd---but, for a given parity
system, always the same). Then, if the total number of 1s is odd
(resp. even), one knows that an
error occurred somewhere.
This is a very simplistic error-correcting code, especially since
it doesn't even correct errors. Much better is hamming code,
where there are enough parity bits to cover each bit of the
message/word multiple times; then, one can determine which
bits are in error by seeing which parity bits are wrong.
Look up algebraic coding theory, information theory, and
other such stuff if you're interested. Hamming wrote about
this stuff, as did Claude Shannon.