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Volatility Smile refers to an Implied Volatility curve where the Options that are in or Out Of The Money have a higher Implied Volatility than the At The Money Options. This effect produces a steeper curve at either extremity, hence the term Volatility smile.

In the classic Black Scholes option pricing model, implied volatilities are even, the curve is straight and does not exhibit the smile shape.

The reason for the deviation from the model is explained by a number of factors, the most common of which is that option prices are affected by market demand for some option contracts. For example, demand for puts may increase to provide protection if one-off events like market crashes are perceived to be more likely (the so called 'black swan' phenomena).
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Contributed by: Ralph Windsor

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