Frame is short for Airframe and is the structure of a UAV craft. Quadcopters are typically made of carbon fiber but some are made of plastic, G10, foam, or some other synthetic materials. Early homemade frames were constructed with wood and towel rack rods.
A typical quadcopter frame will have 4 "arms" that hold brushed or brushless motors at their extremity. Brushless motors are bolted to the carbon directly. Brushed Motors sit in premade "cups" that snug the entire cylinder in place.