Back in the 1930s and 40s, before electric starting technology came into its own, shotgun starters were popular on anything from an aircraft radial engine to a farm tractor.
The way a shotgun starter works is quite simple. A blank shell filled with cordite is loaded into a breech and fired. When fired, the blast from the shell either drives a piston forward that turns the engine over or pushes directly upon one of the engine's pistons, depending on the type of starter.
A Coffman starter and some paper cartridges.
Schematic of how a Coffman works.
Before the days of reliable electric starters and batteries, shotgun starters were the way to go as they were simple, reliable, and lightweight. The obvious drawback was that you needed a supply of shells on hand.
Below are a few videos of shotgun starters in use.
Photo Credits: Starter and Cartridges - keithnewsom Photobucket, Schematic - tradiper Photobucket