Engines that don't have cams in the engine head need some way to transfer the cam's lift to the valves, pushrods are used to make that lift transfer possible. Pushrod engines still have cams, but they are located away from the engine head. The length of the pushrod depends on both the distance between the cam and the rocker arm, and the amount of pressure that needs to be on the valve spring while the valve is closed.
Pushrods usually aren't considered for horsepower gains due to what little drain they have on the overall power of the engine. However, because it is a reciprocating mass, using a lighter material will reduce movement delay of itself, the rocker arm, and most importantly, the valves. When the valves return to the closed position sooner, the engine can run at a higher RPM, or be more reliable at lower RPM levels.
Usually, the main focus of performance pushrods is strength, since they will likely deal with forces that stock pushrods aren't designed for.