Quadriller is a term that means to make criss-cross lines on the surface of food. It is just a way of improving food presentation and making it look more interesting.
It usually refers to food cooked on a grill over top a fire. The bars of the grill burn their lines into the food. You then turn the meat at a 90 or 45 degree angle to create intersecting lines. It can also be done by hand, sort of one line at a time, with a superheated skewer.
It can also be done to ungrilled foods wtih the back of a knife such as fish, scallops, etc.
It can also be used to describe criss-cross strips of pastry on top of a pie, or a criss-cross pattern of anchovies on a pizza, etc.
The effect achieved is called “quadrillage.”