Volatility is degree of variation of trading prices for a given set of returns. Volatility assesses the risk of a security. Volatility can be measured either by standard deviation or variance. Volatility does not measure the direction of price. This is because in standard deviation all difference gets squared. It means even though stocks having same return may give different volatility.
If the stock has more volatility then investors expect more return from such stock likewise if stock has less volatility then investors expect less returns. In other words there is direct relationship between risk and return.