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Volatility is the rate at which security price moves up and down with a specific time horizon.
Volatility is used to admeasure market risk of a financial instrument over predefined period of time, and can be calculated either by using variance between returns of that security and market index or by using standard deviation off the change in value of particular security.

Higher volatility means higher risk involved in a security, because of dramatic fluctuations in price over period of time, usually a year. When calculated by using variance between the security and market index (usually S&P), volatility shows how much a stock moved for every 100% move in the benchmark. If stock's volatility is 1.2, it means that stock moved 120% for every 100% move in benchmark.