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.