"BOSU" stands for Both Sides Up, or Both Sides Used. BOSU exercises - calisthenics basically - supposedly train balance and strengthen the core.
It is challenging just to stand on them (either side is wobbly), but I had to do 3 sets of squats on both sides. It is sort of amusing to watch your legs wobble and vibrate under the effect of the proprioceptive storm.
I'll admit that I could not do all the squats on this thing without a light touch of my trainer's hand. Worth doing? I doubt it but it's more exciting than sitting on a chair or watching TV.
Have you tried it?