Moderate dampening means the ski has some vibration-absorbing materials built in, but it isn't loaded up with heavy metal layers like a race ski. The result is a ski that smooths out chatter and rough snow at typical speeds, yet still feels lively and easy to maneuver when you want to play around.
This is the sweet spot for most skiers. If you spend your days cruising groomers, exploring trees, and occasionally venturing off-piste, moderate dampening gives you enough stability without making the ski feel dead or sluggish. It's forgiving enough for intermediates but still satisfying for advanced riders who aren't charging at top speed every run.
You'd want to look elsewhere if you're a hard-charging freerider who needs maximum smoothness at speed (go high dampening), or a backcountry tourer counting every gram (minimal dampening saves weight). But for everyday resort skiing, moderate is usually the right call.