Example: I have an athlete with the numbers below
Barbell Front Squat (2 Legs) = 285lbs for 6 reps
Barbell Front Split Squat (Single Leg) = 185lbs for 6 reps
Scientific research shows that the front leg gets 90% of the load and the rear leg absorbs 10%
185lbs - 10% = 167lbs Load on his front leg
167lbs x 2 Legs = 334lbs Total load
334lbs - 285lb = 49lbs Bilateral Deficit
Not only are you training each leg to work independent but you're also working the stabilizers of the hip and pelvis, this help prevent strength leakage. Using a small base of support increases proprioceptive input (think balance). If you're strong and have balance on a single leg, imagine how you'll be on two legs!
Add all of these up and you must include unilateral exercises if you are serious about getting everything that you can out of your training program. Some of my favorite unilateral exercises are the unilateral dumbbell alt bench press, unilateral shoulder press, unilateral DB deadlift, rear foot elevated split squat (RFESS) and the unilateral squat (or if you have the strength and mobility a full pistol squat).
Be forewarned, though, since unilateral training will produce some muscle soreness in places that you did not know you had and has also been known to increase performance to previously unattainable levels.