|Vol which is short for Volatility is a measure of how much prices of an asset change.|
From a mathematical point of view, it's the standard deviation (basically the average from the average).
It's used in option calculations, via the Black-Scholes pricing Model.
It is also synonymous with Risk. A common way that risk is measured is via the Sharpe Ratio with is the annualized returns divided by the annualized Standard Deviation. The annualized standard deviation is the daily deviation multiplied by the square root of 365. Note that 250 is commonly used but that only applies when the asset is traded on business days.