NON-BIASED DEFINTION: In recent years, in the U.S. only, a red state has come to mean a state that traditionally votes Republican, as opposed to a blue state which traditionally votes Democrat.
In the past, media would use maps with red for one party and blue for the other, with no set standard. The current trend was set during the 2000
Presidential election, when NBC used it. The race was very close, and
because of this, Tim Russert was often heard to say things like "Bush needs x more red states in order to win, and Gore needs x more blue states in order to win." Because the coverage was being watched so intently by so many people, the color scheme stuck, and is now used by all networks.
What many people don't realize is that this color scheme is actually the opposite of traditional political colors. Red has always been associated with socialism and communism (i.e. extreme forms of liberalism) as seen on flags of countries such as the P.R.C., the U.S.S.R., and the D.P.R.K. On the other hand, blue is most often associated with
conservatism, and sometimes facism (i.e. the extreme form of
conservatism). Most nations still use this color scheme.
It may be that NBC assigned these colors at random, or it may be because Republican and red both start with R. Neither party has
officially adopted these colors. This color scheme has often led to confusion when residents of other countries see a political map of the U.S. or hear Americans discussing red states versus blue states.