[koh-vair-ee-uh
ns] 
| the expectation or mean value of the variable formed by multiplying the differences obtained by subtracting two given variates from their respective means; the product of the standard deviations of two given variates and the coefficient of correlation between them. |
| co·var·i·ance (kō-vâr'ē-əns) n. A statistical measure of the variance of two random variables that are observed or measured in the same mean time period. This measure is equal to the product of the deviations of corresponding values of the two variables from their respective means. |
Covariance
A measure of the degree to which returns on two risky assets move in tandem. A positive covariance means that asset returns move together. A negative covariance means returns vary inversely.
One method of calculating covariance is by looking at return surprises (deviations from expected return) in each scenario. Another method is to multiply correlation between the two variables by the standard deviation of each variable.
Investopedia Commentary
If you owned one asset that had a high covariance with another asset that you didn't own, then you would receive very little increased diversification by adding the second asset. Of course, the opposite is true as well, adding assets with low covariance to your portfolio lowers overall portfolio risk.
Related Links
Introduction to Value at Risk (VAR) - Part 1
Introduction to Value at Risk (VAR) - Part 2
See also: Correlation, Modern Portfolio Theory, Standard Deviation
covariance