Body-on-frame is an automobile construction technology. Mounting a separate body to a rigid frame which supports the drivetrain was the original method of building automobiles, and its use continues to this day. The original frames were made of wood (commonly ash), but steel ladder frames became common in the 1930s.
In the USA the frequent changes in automobile design made it necessary to use a ladder frame rather than monocoque to make it possible to change the design without having to change the chassis, allowing frequent changes and improvements to the car's bodywork and interior (where they were most noticable to customers) while leaving the chassis and driveline unchanged, and thus keeping cost down and design time short. It was also easy to use the same chassis and driveline for several very different cars. Especially in the days before computer-aided design, this was a big advantage. 
Most small passenger vehicles switched to unibody construction in the 1960s, leaving just trucks, buses and large cars using conventional frames. The switch continued for several decades - even SUVs typically use unibody construction today. Body-on-frame remains the preferred construction method for heavy-duty vehicles, especially those which are intended to carry and pull heavy loads.
Advantages and disadvantages compared to unibody
- Generally more comfortable because fewer vibrations from engine and wheels reach the driver
- Easier to design, build and modify (less of an issue now CAD is commonplace)
- More suited for heavy duty usage and more durable
- Easier to modify
- Heavier than unibody
- Center of gravity is usually higher
- Less resistant to torsion (flexing of the whole car in corners)