A slipper clutch is basically a one way clutch. It grips or holds when you are accelerating and slips when you roll off the throttle so the engine braking doesn't cause the rear wheel to lock-up. Twins and I guess singles are more prone to rear wheel lock up when you roll off the throttle in lower gears or downshift to a lower gear. Your R1 does it too but it is not as dramatic as a twin. Aprilia and other manufacturers design slipper clutches to reduce this effect. Aprilia's method is to use engine vaccum to activate the slipper mechanism, while others basically use a spring ramp type design.
What you basically need to know about it is, umm nothing. I don't say that to be rude, its just that the system works invisibly, you don't notice it and you don't need to worry about it. The only people who would notice anything are those accustomed to pwerful engine braking on other twins. You seem really interested in the bikes, check out a few dealers in your area as they are usually pretty good about giving demo rides. When you ride the bike you will still feel more engine braking than your R1, but considerably less than you would on another twin without a slipper clutch.
Good luck,
Gregory
I could have been a squid, but I was too busy posing.