Cut

When a diamond is cut with ideal proportions (for its shape), more light reflects out the top of the gem
producing incredible fire and brilliance.
A poorly cut diamond, on the other hand, looks dull and lifeless because incongruous proportions allow light to escape out the bottom and sides.
In short, a well-cut diamond will be much more brilliant because it reflects and refracts light better than one not cut as well. A better cut is more rare, more desirable, and therefore, will command a higher price.