Standard deviation.
In plain English
Standard deviation is a statistical measure of dispersion: how widely a set of numbers (in finance, usually returns) varies around its average. A small standard deviation means returns cluster near the average; a large one means they range widely. In investing, annualized standard deviation is the most common quantitative measure of volatility. Roughly two-thirds of returns fall within one standard deviation of the mean, and about 95% fall within two. This assumes returns are normally distributed, which in finance they often are not, but the approximation is still useful.
01Why it matters
Standard deviation is the building block of nearly every risk-adjusted return measure (Sharpe ratio, information ratio, etc.). It is also the most common honest answer to 'how risky is this fund?' that gets reported in prospectuses and fund fact sheets.
02The math, step by step
The S&P 500 has a historical annualized standard deviation of about 15% to 20%. A one-year return within +/-15% to 20% of the long-run average (10%) is therefore statistically normal. Returns outside that range happen every few years.