They are a system to reduce ball chopping by the bolt inside the gun. There are two types, break-beam and reflective, but they both accomplish the same task. They are located below the feedneck in the breech of the gun, and are used by the electronic board in the grip to determine if a paintball is fully seated in the breech. If a paintball is not detected, it will not fire the gun even when the trigger is pulled; this avoids the ball being chopped in half when the bolt moves forward to fire the ball.
You'll shoot just as fast. It might seem like you're going faster otherwise if you have your eyes closed, but when you look you'll see yourself spraying chopped paintballs everywhere.
For more shooting speed, practice and buy a better loader once you outgrow yours.
To say you can shoot as fast is a lie. Some boards will limit the ROF if the eyes aren't on. Some won't. Usually turning eyes off will be faster (the gun doesn't have to disregard a shot if there isn't a ball in the chamber) but then you're most likely going to chop, which will make it a lot slower.
Basically, eyes are good things for paintball gun.