Decibels and intensity

The intensity of a sound is a measure of the strength of the sound wave as it is indicative of the energy transported by the wave to a specific unit of area.  Recall that

sound intensity is proportional to the square of the amplitude of the sound wave AND
amplitude is a measure of the pressure changes associated with the wave.

The commonly used measure of sound level is the decibel (dB).  
Sound level in decibel is calculated using the sound intensity (I) relative to a reference intensity (I0).  
β (Db) = 10 log I 
I0

The reference intensity is usually the lowest (or threshold) intensity of sound that a person with normal hearing can perceive at 1000 Hz.
(I0 = 10–12 W m–2)

The logarithmic relationship and the factor of 10 are used because our ears are not very sensitive to changes in intensity. 
For example we perceive a loud rock concert to be twice as loud as a loud conversation whereas the ratio of the sound intensities is actually a factor of 1 million.