A rainbow option is a derivative whose value is dependent on two or more underlying securities or events. An example of a rainbow option would be an outperformance option which allows an investor to exchange one stock for another. In this case, the investor's decision to exercise the option is dependent on the price of both stocks.
For example: An option which allows a person to exchange 10 shares of Morgan Stanley for 1 share of Goldman Sachs would be a rainbow option. The option holder would gain if Morgan Stanley shares fall in value relative to Goldman shares, and lose if they relatively increase.
Rainbow options are useful for hedging risks arising from several events. The price of the rainbow option, to a large extent, is dependent on the correlation of the underlying events or assets -- with lower correlation leading to higher prices.