Brilliance
The white light reflected back to the viewer from inside a gemstone, which makes it look bright.
Where brilliance comes from
Diamond has a high IOR of about 2.42, which bends light strongly and gives it a small critical angle of about 24 degrees. When the pavilion angles are right, light hitting the lower facets reflects inside the stone instead of escaping, and it leaves through the table and crown. Cut a pavilion too shallow or too deep and light leaks out of the bottom, so the stone looks darker.
Brilliance, fire and scintillation
Brilliance is one of three effects people describe as sparkle. Fire is the coloured flashes from dispersion, and scintillation is the pattern of flashes as the stone moves. A beautiful diamond balances all three.
Getting brilliance right in renders
A render can only show brilliance when three things are true. The stone mesh has accurate proportions, the material uses the correct IOR, and the environment contains both bright light sources and darker areas. Stones reflect their surroundings, so a flat white environment produces a flat, grey stone.
In the RenderMyJewels studio, the gem environment is chosen separately from the metal environment. That lets you pick a high contrast environment that brings stones to life while keeping a softer one for the metal. Compare a few gem environments on the same ring, because the difference is easy to see in a close-up.