What is Volatility Swap?

Legal Definition
In finance, a volatility swap is a forward contract on the future realised volatility of a given underlying asset. Volatility swaps allow investors to trade the volatility of an asset directly, much as they would trade a price index.

The underlying is usually a foreign exchange (FX) rate (very liquid market) but could be as well a single name equity or index. However, the variance swap is preferred in the equity market because it can be replicated with a linear combination of options and a dynamic position in futures.

Unlike a stock option, whose volatility exposure is contaminated by its stock price dependence, these swaps provide pure exposure to volatility alone. This is truly the case only for forward starting volatility swaps. However, once the swap has its asset fixings its mark-to-market value also depends on the current asset price. One can use these instruments to speculate on future volatility levels, to trade the spread between realized and implied volatility, or to hedge the volatility exposure of other positions or businesses.
-- Wikipedia
Legal Definition
A swap that exchanges realized volatility for fixed volatility. It directy protects the asset or market. This can last 6 months to 5 years.