It is all relative, really.
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The decibel indicates sound intensity, relative to a known reference (usually 0dB). A positive value means it is greater than the reference (magnified), a negative means it less than the reference (attenuated).
For example: on many TV or home audio systems, when you increase the volume, you might see the volume meter in decibels count up from some negative value to 0dB. In this case, the "max" volume that the TV can go to is 0dB (reference value) and any signal below that (when you turn down the volume) is considered negative.
On pro audio equipment, you might see attenuator knobs which have 0dB, -10dB, or -20dB settings. If you input signal is too strong, you can attenuate it by some amount (make it less strong).
Mathematically, a decibel is:
10 * Log ( P1 / P0 )
Where P1 is the sound intensity (many different units for this) of whatever you are measuring, and P0 is the reference.
Essentially, this means that for 10dB increase in signal, the signal is 10 times more intense. For a -10dB loss, the signal is 10 times LESS intense. Because it is logarithmic, however, a 2 times change in signal (say, from an intensity of 5 to an intensity of 10) is a 3dB change, not 2dB.
Also check out the wikipedia article:
http://en.wikipedia.org/wiki/Decibel