In road vehicles the power-to-weight ratio is often used as an indication of likely accelerative performance. Vehicle weights have relatively little impact on top speed, which is mostly dependant on aerodynamic drag, which is proportional to the square of the vehicle speed (see drag equation). Acceleration, on the other hand, is dominated by the Newtonian acceleration term, P = ma, so more power (P) will deliver more acceleration (a) for any given vehicle weight (m).
In an aircraft, any additional weight requires more lift to be generated by the wings in order to lift it. More lift from the wings automatically means more drag, through a process known as induced drag, slowing the plane down. Thus if any two engines deliver the same power, the lighter one will result in a faster plane. Power-to-weight ratio therefore has a much more important impact on overall performance in aircraft, including top speed.
In this usage the power-to-weight ratio is typically used to refer to the weight of the engine alone, as a useful way of comparing various aircraft engines. The term applying to the aircraft as a whole is power loading.