Cork grips are a favorite among touring and backcountry skiers primarily because of how they handle moisture. When you're skinning uphill for hours, your hands naturally sweat, and cork does an excellent job wicking that moisture away, keeping your grip secure and your hands drier than rubber or plastic would.
Another nice benefit is that cork gradually molds to the shape of your hand over time, giving you a custom fit that gets more comfortable the more you use it. It also provides decent insulation, so it doesn't feel icy cold on early morning starts like plastic grips can.
The main downside is durability—heavy use can cause cork to wear down or even crumble after a few seasons. But for skiers spending long days in the backcountry, that trade-off is usually worth it for the comfort and moisture management. If you mostly ski resort laps, rubber grips are perfectly fine and tend to last longer.