A diamond is cut in such a way that the flat shape of the crown allows for the maximum number of light rays to either reflect off the crown or refract into the diamond.
The critical angle of diamonds will be small as the refractive index of diamond is high.
The shape and angle of the pavillion is such that most light rays falling on it will have an angle of incidence greater than the critical angle. This allows for total internal reflection to occur, causing light rays to reflect multiple times within the diamond, and leave the diamond through the crown.
The multiple light rays leaving the crown of the diamond makes it look more brilliant to an observer looking at the crown of the diamond.