A flat alpine ski has a clean, smooth deck with no pre-installed binding tracks or plates. Instead, alpine bindings are drilled and screwed directly into the ski by a shop technician. This is the most common setup for performance and freeride skis.
The big advantage is versatility—you can mount virtually any alpine binding you want, and you get the most direct power transfer from boot to edge. That's why racers and aggressive skiers prefer it. You're not locked into one brand's system.
The trade-off is that you'll need a professional mount, and once those holes are drilled, remounting a different binding means punching new holes. If you're a resort-only skier who wants the best performance and doesn't mind committing to a binding, flat alpine is the way to go.