In theater, wagons are usually rigid platforms which rest on casters instead of legs. Sometimes instead of rigid platforms parallels are used. The size of wagons varies from less than a foot square to so large that the entire set can fit on them. A slipstage is a huge wagon which is just a little bit bigger than the playing area of the stage. A slipstage holds the whole set and allows the property crew and set crew to move the entire set on and off the stage by pushing and pulling the wagon.

Casters can be either swivel or rigid. They’re a type of wheel, which are small. Many beds and other household furniture have them on the frames. On wagons casters are usually bolted onto caster plates which are attached to the bottom of the platform. The caster plates should be tall enough to allow an half to three-fourths of an inch of clearance between the bottom edge of the platform and the stage floor. Casters should generally not be spaced more than forty-eight inches apart. This is to prevent the platform from bouncing when it is walked on. If the platform framing is very stiff such as when a two by six or two by four is reinforced with one and a half to two inch by three-sixteenth of an inch or one forth of an inch mild-steel straps, the casters can be placed a little farther apart without causing a problem.

Wagons are sometimes made out of stressed-skin and honeycomb-laminate platforms. The mounting bolts for the casters on both of these types of platforms need to penetrate both skins in order to ensure a strong attachment. A caster mounting jig and bearing plate can be used as a way of increasing the strength of the caster mount.

Wagons make moving large props and scenery much easier to do. If the wagons are made well they can be moved, even with a heavy load without making much if any noise audible to the audience.

Wagons are often called dollies in various parts of the world.


Sources:
Limited experience in a scene shop
Gillette, J. Michael. Theatrical Design and Production. 4th ed. Mountain View: Mayfield, 1999.
SharQ and La petite mort, thank you for pointing out to me that they are also called dollies.