The bore relates to the diameter of the cylinder walls, while the stroke refers to the length at which the piston travels in the combustion chamber. Bigger bore and stroke ratios are often used in unison to create a balanced and powerful engine.
The bore and stroke ratio is often used to decrease the piston movement speed inside of an engine.
An oversquare engine has a bigger bore than stroke. Pistons of these engines having shorter stroke ratios, and because of that tend to create more power in the higher rev ranges. The shorter stroke also impacts the speed of the piston and slow them down. Engines with large bores will eventually require larger valves to allow better volumes of air to travel through. Because of their high revving capabilities, oversquare engines are used frequently by Formula One racing cars and motorcycle companies.
An undersquare engine has a longer stroke and smaller bore. This lessens the size of the bore, which also decreases the number of valves available to be mounted in the engine's head. Undersquare engines have their power peak in the lower rev ranges.
An engine with a well balanced bore and stroke ratio is called a square engine. These motors bring the bore and stroke ratio to approximately 1:1.