HB
The bosu ball is a semi-sphere on a solid plastic basis that you can use on both sides. Both rounded and flat.
By having an unstable base, you can use it to tone the musculature, especially the abdominal abs. It is a really useful accessory for many types of training: cardiovascular, musculation/fitness, pilates, yoga, crossfitetc.
On the other hand, the rigid base will help you to exercise balance and coordination.