A dolly is a small, handheld anvil used for doing auto body repair. It is used both as a hammer, to push up low spots, or as an anvil, resting on low spots while you hammer down high spots. A good dolly is forged, not stamped, and polished for maximum smoothness. Like an anvil, any pockmarks or ridges in its surface will be transferred to any surface hammered upon it.
Dollies come in a variety of styles. The most common is the rail dolly, which resembles a piece of a piece of rail such as a train would ride upon; It has a rounded upper portion, it tapers toward the middle, and then has a broad, flat or nearly flat bottom. A completely flat-bottomed rail dolly is called a shrinking dolly, and it is used (as its name implies) for shrinking stretched metal, which involves the use of heat.
There are also heel and toe dollies, shaped like the heel or toe of a boot, respectively; comma dollies, shaped like a comma which has been extruded a few inches; and any number of other designs. If you can conceive of a blob-like shape in your head, which features sharp and smooth curves and maybe a flat spot, it has probably been forged or stamped by someone as a dolly at some time in the past.
A dolly is also a cart which is built extremely low to the ground; In fact in many cases the frame of the cart is actually dropped below the axles on its wheels or casters. For instance, one might put a car on four wheel dollys so it can be rolled sideways on a concrete shop floor.