Stabilized wood is a softer wood that has had its structural integrity reinforced by being impregnated with some kind of additive.
For example, burls are essentially the scars that form where a tree is subjected to some kind of abuse - their naturally forming as a result of some kind of virus or bacteria, or artificially induced by physical damage to the tree. Unlike ordinary wood, the grain in burl wood is erratic and doesn't hold the wood together very tightly. At the same time, the grain in burl wood can be very interesting. Natural burl wood is hard to turn because the random fibers don't hold it together well. But it can be reinforced by impregnating the wood in a compound that essentially glues the fibers together.
Likewise, spalted wood is a hardwood that has a fungal growth that is interspersed between the grain. It's a beautiful wood, but it can also be a bit 'punky' because spalting is an early stage of rot. Again, impregnating the wood with some kind of resinous compound can strengthen the wood so that it can more easily be turned and finished.
Commercially stabilized wood is more expensive than conventional wood. The reason people choose to purchase it is that the grain patterns can be more dramatic and interesting.
If you are just starting out, you probably want to learn on less expensive wood and leave the stabilized stuff for when you acquire some skills.
