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Duration is another way to measure bond volatility. Duration is a measure of how much the price of a bond changes when compared to its interest rate. Bond price will change from time to time as the issuing organization evaluates the value of the bond on the market.
Variance is a measure of distribution of returns and is not neccesarily bound by any time period. Volatility is a measure of the standard deviation (square root of the variance) over a certain time interval. In finance, variance and volatility both gives you a sense of an asset's risk. If the mean is the average return of an asset, variance and volatility can give you a sense of how much that asset either overperforms or under performs.