A drone frame is the structure that holds a drone together.  It's the skeleton that all other components are mounted on.  The frame protects the sensitive electrical components of the quadcopter.  It also supports the motors and other electronics, and prevents them from vibrations. 
A drone frame must be structurally strong and aerodynamically efficient. The most common materials for drone frames are: 
Carbon fiber: The strongest and lightest material, but also the most expensive and brittle.
Plastic: The cheapest and most flexible material, but also the heaviest and weakest.
Aluminum: A common material.
There are three different types of drone frames: 
Racing frames: Designed for high-speed, agile flying, and are typically small and lightweight.
Freestyle frames: Designed for more versatile, acrobatic flying, and tend to be larger and more durable.
Long-range frames: Designed for extended flight times and are usually larger and more stable.
The most common frame size is around 210mm, which most people would refer to as a 5 inch frame