Brilliance is an essential attribute of a beautiful diamond and has 2 components; brightness and contrast. Bright diamonds return lots of light from the surroundings back to a 'face up' an observer. If light from above leaks out the back of a diamond, naturally it has less brightness. But light that enters and leaves in the face up direction is wasted because your head blocks lights from that direction. Diamonds that are too deep or very shallow do this –they have areas that act like a mirror back to the viewer; they return less light and so they have less brightness.
But to be brilliant, a diamond needs more than just brightness from light return. Consider the contrast of a chess board, although it has only 1/2 the light return of a sheet of white paper, it appears brighter, especially when it is moved because it 'scintillates'.
Fire or dispersed light appears as flashes of rainbow colors. You see more fire in darker environments like restaurants that have just a few point light sources or a flickering candle.
Diamond experts have known for a long time that steep crown angles and small tables (like 'old cut' diamonds) produce more fire. But this combination also produces less light return. Less light return makes it easier to see firey flashes that might otherwise be swamped by bright white sparkles; that one reason is why old cut diamonds and some fancy cuts appear to have a lot of fire.
Scintillation is the intense sparkles in a diamond as it moves. Black and white sparkles of scintillation show well in flood lit or office lighting environments where fire can be totally absent. Under pin point or spot lights fire also adds to scintillation. Ideally a diamond has many pleasing flashes spread across the surface of the stone, with few dull dead patches.
A moving chess board appears 'brighter' than a sheet of white paper that has only half the light return.
There are 2 causes of diamond contrast. Leakage can contribute to good contrast, e.g. the small leakage areas that are commonly seen around the girdle of a diamond with an ideal-scope (on the left). Secondly the observers head and body obstruct light sources and can cause the contrasting star (on the right) as a result of the relative darkness of the observers head (mimicked by the lens of the Ideal-Scope).