If you plot the implied volatility of options across strikes (for one expiration), you rarely get a flat line. Often you get a U-shape — higher IV for deep out-of-the-money puts and calls, lower in the middle. That curve is the volatility smile. It reveals that the market prices tail risk into the wings.
Why the smile exists
The classic Black-Scholes model assumes a single, constant volatility and normally-distributed returns. Reality disagrees: markets have fat tails — extreme moves happen more often than a normal distribution predicts. So traders bid up the price (and thus implied volatility) of far-out-of-the-money options that pay off in those extreme moves. The smile is the market correcting the model's tail blindness.
Smile vs skew
The smile and skew are related views of the same surface. A symmetric smile (both wings elevated) reflects tail risk in both directions. In equity indexes, the curve is usually lopsided — a skew — with downside puts far more expensive than upside calls, because crashes are faster and hedging demand is one-sided. The "smile" often looks more like a "smirk" in stocks.
The volatility smile is the options market saying, out loud, that the tails are fatter than the textbook admits.
Why it matters
The smile shapes what you pay: far-OTM options are relatively expensive because their IV is elevated. It also feeds dealer positioning and how the tape behaves near big strikes. You don't need to trade the surface to benefit — just to know that "cheap" and "expensive" options are priced by a curve that already respects tail risk, not by distance-from-strike alone.