Triple BOA gives you three independent dials to control three separate zones of the boot—usually the lower forefoot, midfoot, and upper ankle/cuff. This lets you micro-tune tension exactly where you need it, which is why it shows up mostly on high-end freeride and aggressive all-mountain boots. If you're charging steep, technical terrain or riding at high speeds where precise response matters, that extra adjustability can make a real difference in heel lock and overall control.
For most resort riders and park riders, triple BOA is probably more than you need. Double BOA already gives you solid upper and lower zone control, and it's lighter and simpler. Triple BOA adds a bit of weight and more moving parts, so if you don't have a specific fit issue—like a narrow heel with a wide forefoot—you likely won't notice the benefit. It's also worth remembering that more dials means more potential points of failure, so always pack a spare dial on longer trips.