Polished crystal spheres are popular for many different reasons.
They are beautiful to look at and aesthetically interesting because, especially in the cases of transparent or translucent crystals, they often enable one to view the structure of the crystalline material including formation layers and perhaps inclusions or other discontinuities. They are sometimes used decoratively in homes and offices. They are also used by some people for energy balancing - usually to encourage even distribution of 'earth energies' around the surrounding space.
The most famous application of crystal spheres, or "crystal balls", is screeing - as practised by traditional fortune-tellers. However, only the larger sizes of crystal spheres tend to be used in this way and they can be very expensive. Some psychics prefer to use glass spheres rather than clear quartz for this purpose.
See also the main IvyRose Holistic section about Crystals & Gemstones.