In finance, what volatility means often depends on the context. The most general definition of volatility is associated with the range or unpredictability of returns. A more volatile security will have had or will be expected to have a wider range of returns. All else being equal, more volatile securities are considered to be more risky. All else being equal risk averse investors will prefer less volatile investments.
In risk management, in everyday use, volatility is often synonymous with standard deviation. Because standard deviation has a specific mathematical definition and because volatility can be used in a more general sense, standard deviation is considered to be the more technically precise term.
When dealing with options, volatility or “vol” is often used as shorthand for implied volatility.