Standard deviation measures how widely a set of returns is spread around its own average. A low standard deviation means returns cluster close to the mean (a steady ride); a high one means they are scattered widely (big ups and downs). It is the statistic that underpins the everyday idea of volatility.
Why it is the core risk number
In finance, standard deviation of returns is the most common single measure of risk, because it captures the size of the swings you have to endure to earn your average return. It feeds directly into other tools: the Sharpe ratio divides excess return by standard deviation to judge reward per unit of risk. One limitation to keep in mind is that plain standard deviation treats upside and downside swings the same, even though most investors only truly worry about the downside.