Guilloche is the French for "engine turning".  Engine turning is the mechanical engraving of lines on metal to create a design.  The engraving causes the reflection of light through the overcoating of transparent enamel  to be enhanced.  This causes a brilliance which can be seen as the piece is moved from side to side. This style of enameling was brought to prominence by Fabergé when showing pieces in Paris in 1900.