High dampening means the ski is built to absorb significant vibration and chatter, usually through metal layers like titanal built into the construction. This keeps your skis glued to the snow and feeling smooth even when you're flying down choppy terrain at high speeds.
You'll want high dampening if you're an aggressive skier who charges hard, races, or regularly skis fast on variable snow. It's the difference between driving a sports sedan versus a go-kart—stable and planted versus lively and twitchy.
The tradeoff is weight and playfulness. Highly dampened skis tend to be heavier and less nimble at slower speeds, making them feel sluggish if you're mostly cruising groomers or skiing at a moderate pace. If you're not regularly pushing the speed limit, moderate dampening will give you a better balance of smoothness and agility.