Black-Scholes assumes a stock has a single volatility. But if you take real option prices and ask "what volatility would the formula need to produce this price?" — the implied volatility — you get a different answer for every strike. Plot implied vol against strike and the curve smiles (or, for stocks, smirks).
Why the curve isn't flat
Because the real world has fat tails and crashes that the neat bell curve ignores. Investors pay up for downside protection, so out-of-the-money puts carry a HIGHER implied volatility than at-the-money options. In equity indexes this shows as a downward skew — the famous shape that appeared right after the 1987 crash and never left.
What it actually tells you
The smile is the market's confession that Black-Scholes is incomplete — and a map of where fear is priced. Rich downside puts are exactly why selling them (put-writing) earns a premium: you're paid for insuring the crash the smile is worried about (see PutWrite Income). That premium is real, but it is compensation for risk, not a free lunch — the smile also tells you when insurance is expensive because trouble may be near.
How pros use it
Traders quote and hedge off the whole volatility surface (smile across every expiry), not a single number. It's descriptive plumbing — knowing the smile exists does not, by itself, give a retail edge.
Educational material — not investment advice.