Implied volatility is the annualized volatility number that, plugged into an option pricing model, reproduces the option's current market price. It is the market's forward-looking price of movement, quoted in percent per year.
An IV of 30% on a $100 stock prices roughly a ±30% range for one year at one standard deviation, scaling with the square root of time: about ±8.7% over a month. IV is solved from prices, not observed, so it inherits every quirk of the quote: each strike and expiration carries its own IV (the smile and term structure), and stale or wide quotes produce unreliable IV. Because United States equity options are American-style, careful solvers strip the early-exercise premium before backing out IV; skipping that step distorts in-the-money puts most.
The volatility an option's market price implies when it is put back through a pricing model. It is the market's forward estimate of how much the underlying will move, expressed as an annualized percentage, not a record of how much it has moved.
Historical volatility is measured from past prices; implied volatility is priced from option quotes and carries a premium for uncertainty and for the convexity option buyers hold. The gap between them is the volatility risk premium, which the net volatility risk premium page turns into a single number.
Multiply the annualized IV by the square root of the fraction of a year until expiry and by the stock price. For a stock at 100 with 30 percent IV, one standard deviation over 30 days is about 100 times 0.30 times the square root of 30 over 365, roughly 8.6 points.