The standard calculation takes daily log returns over a window, computes their standard deviation, and scales by the square root of 252 trading days. Different windows and different estimators produce noticeably different numbers, so always check which is being quoted.
Realised volatility is the settlement price of every volatility trade. Selling options at 25% implied is profitable, after hedging costs, only if the underlying goes on to realise less than 25%. Everything else — skew, term structure, positioning — is detail around that comparison.
Example: XYZ moved an average of 0.9% a day over the past 20 sessions. Annualised, that is roughly 14% realised volatility. With 30-day options implying 25%, a hedged seller is being paid 11 points for risk that has not yet shown up.
Related: implied-vs-realized, variance-risk-premium, gamma-scalping, volatility-cone