Sound Pressure   

Very small and rapid fluctuations in atmospheric pressure detected by the ear and processed by our neural systems result in the perception of sound. 

These fluctuations are the same phenomena as that detected by a barometer. 

The difference between these two is that the ear is sensitive to much smaller and rapid fluctuations than those detectable by the barometer. 

On the other hand we do not hear changes in the weather! Even though these much greater but slower changes in atmospheric pressure are taking place in our environment all the time. This is because the frequency and wavelength of these great Gain fluctuations are too great to be detected. In effect they fall outside the range of human hearing
The ear is actually affected by these changes, but more in the sense of a DC offset being applied the eardrum which is self-corrected by a pressure equalization mechanism in the ear itself. The closest we come to registering such global pressure changes is when we experience "popping" of the ears, a result of this self-correction after a relatively rapid change of altitude such as experienced during air travel or driving up and down mountains. 
Returning to the sound pressure fluctuations we can hear, one can think of them by analogy to a stone dropping into a pool of water. Just as the waves in the water radiate away from the place where the stone was dropped so sound pressure waves radiate away from the source of the sound.  Sound intensity is proportional to the square of the sound pressure, making the calculations for each slightly different when using the decibel system of measurement
sound pressure level     intensity