Why is it important to balance the braking between the front and rear tires?

On a bike it's not really that important, as a bike will have most of its braking capacity on the front wheel as long as traction is good. But if you're riding on loose gravel or similar you'll slow the bike down the fastest if both wheels are just on the edge of locking up. The balance bit comes in due to something called dynamic weight transfer. Basically this means that because of inertia the front will become heavier and the rear will become lighter as the brakes are applied, and the less weight there is on a wheel the less braking it can do before it locks up. So as you brake you'll have to back off on the rear brake or the rear will start skidding.