Why concave facets?

They are certainly lovely, but what specifically and technically do
they achieve over standard facets? 

Ann, Due to the curved nature of the cut surface, the gem material
acts as a lens, focusing the incoming light. This style is also
called OMF - Optically Magnified Faceting. The curved facets are
VERY bright.

Frank Romano
“Gemcutters are Multifaceted Individuals”
http://www.romanogems.com