Before 1987 equity options were priced with a roughly flat smile. After it, the market permanently repriced downside tails, and today every equity chain shows puts richer than equidistant calls. The skew is both a memory of gap risk and a supply-and-demand artefact: everyone wants protection and few want to sell it.
Skew changes how every structure prices. It makes put spreads cheaper to sell and more expensive to buy, it makes zero-cost-collars asymmetric, and it means delta-as-probability overstates the true chance of a large fall. Trading against the skew is trading against a persistent, well-paid insurance market.
Example: XYZ at $50 with 45 days to expiry. The $45 put implies 41% volatility while the $55 call implies 29%. Same distance from the money, twelve points apart. That gap is why the $45 put costs $0.90 while the $55 call costs $0.55.
Related: volatility-smile, volatility-surface, risk-reversal, skew-index