Volatility skew (or volatility smile) refers to the fact that implied volatility for strike prices below the current price of an underlying asset are higher than the implied volatility for strike prices above the current price of the underlying asset.
Volatility skew leads to the phenomenon where implied volatility rises when markets fall and falls when markets rise. This inverse relationship between IV and the underlying asset is thought to stem from the fact that traders believe bear markets are riskier than bull markets. This explanation is only partly true as traders believe the risk to their portfolio is higher in bear markets than in bull markets. The skew in implied volatility is actually an artifact of the bidding process that occurs on exchanges and has come about since the October 1987 stock market crash. Since Black Monday, traders have continuously bought out of the money puts as portfolio insurance to protect against another catastrophic decline. This constant buying of puts drives up the price as their is a greater demand. As all other option variables are the same, the increased demand for puts and higher prices is manifested in a higher implied volatility. To compound this process, it is also common for trades to sell out of the money calls to generate income. The increased supply of calls from the writing of covered calls lowers the price and this lower price is manifested in a lower implied volatility. These artificially higher (for puts) and lower (for calls) volatilities are transferred to the inverse option according to put-call parity leading to higher implied volatility for strike prices below the current price of the underlying and lower implied volatility for strike prices above the current price of the underlying thus creating volatility skew.