A sound source radiates power and this results in a sound pressure. Sound power is the cause. Sound pressure is the effect. Consider the following analogy. An electric heater radiates heat into a room and temperature is the effect. Temperature is also the physical quantity that makes us feel hot or cold. The temperature in the room is obviously dependent on the room itself, the insulation, and whether other sources of heat are present. But for the same electrical power input, the heater radiates the same power, practically independent of the environment. The relationship between sound power and sound pressure is similar. What we hear is sound pressure but it is caused by the sound power emitted from the source.
Too high a sound pressure may cause hearing damage. So when trying to quantify human response to sound, such as noise annoyance or the risk of hearing loss, pressure is the obvious quantity to measure. It is also relatively easy to measure: The pressure variations on the eardrum we perceive as sound are the same pressure variations which are detected on the diaphragm of a condenser microphone.
The sound pressure that we hear, or measure with a microphone is dependent on the distance from the source and the acoustic environment (or sound field) in which sound waves are present. This in turn depends on the size of the room and the sound absorption of the surfaces. So by measuring sound pressure we cannot necessarily quantify how much noise a machine makes. We have to find the sound power because this quantity is more or less independent of the environment and is the unique descriptor of the noisiness of a sound source. (from Bruel & Kjar)