The well-known example on what sound power is, is of course the heater example.  A heater radiates heat in the room (cause) and the temperature of room rises (effect). In the acoustic world this translates in to sound power as cause and sound pressure as effect.  By measuring sound pressure levels, you can determine if a pressure level is as expected. Perhaps individuals are exposed to too high a pressure level, e.g., in a factory or in the construction world. Or the other side, may I install an additional speaker array in my concert hall.

Sound Power comes into play after determining sound pressure levels. If you want to know the cause of the sound pressure level, you will have to determine the individual power of the sound sources. You do that with sound power.