Under sticky strike, the $50 line stays at 25% whether XYZ is at $49 or $51. Because the at-the-money strike changes as price moves, the at-the-money volatility slides along the existing volatility-skew — a fall raises it, a rally lowers it.
This assumption matters for hedging. Under sticky strike a long put position picks up extra profit in a decline, because the option you own moves toward the money where volatility is higher on the curve. Assuming the wrong regime gives you the wrong vanna and the wrong hedge.
Example: XYZ at $50 with the $50 strike at 25% and the $47.50 strike at 28%. XYZ falls to $47.50. Under sticky strike, the new at-the-money volatility is 28% because the $47.50 line did not move.
Related: sticky-delta, volatility-skew, vanna, volatility-surface