A measure of the variation in price over time. Also a measure of the risk of a financial instrument.
Historic volatility is derived from time series of past market prices. An implied volatility is derived from the market price of a market traded derivative (in particular an option).
It is common for discussions to talk about the volatility of a security's price, even while it is the returns' volatility that is being measured. It is used to quantify the risk of the financial instrument over the specified time period. Volatility is normally expressed in annualized terms, and it may either be an absolute number ($5) or a fraction of the mean (5%).