The db scale is actually a measurement of difference between two values. It's sort of like weight- you can't measure the difference in weight between two objects, unless you have 2 objects- measuring the weight difference between My TV and My TV doesn't work too well.
If you dont have 2 values specifcally to measure- you need to declare a 2nd value as a reference value against which everything will be measured, in order to measure in decibels.
As such, a reference value is created- and the intensitey you wish to measure is weighed against that reference.
When the two intensities are equal- the ref value and the tested value- the math works out to be, essentially, 0db. If your tested value ends up lower than the ref, then it would be a negative number. So your DB scale is measuring your current power in relation to a given ref point.
So, if you choose the "maximum" intensity (or the max you'd want it to perform at) as your ref value, which is the standard in many cases, then the DB scale becomes sort of a measure of potential. Most intensity you seek to measure will be either be equal to or less than that maximum, thus the negative scale.
When measuring the quality of audio circuits, there is usually a reference level, referred to as zero dB (decibels). Good quality means a uniform, or flat, response and poorer quality means degradation of the response at certain frequencies. Degradation is expressed as negative decibels, accentuation (also undesirable except for tone controls) is expressed as positive decibels.