I know it’s a sophomoric question but I’ve never understood it. How can there possibly be a negative dB rating? Common sense dictates that 0 dB should be dead silence. So, what gives? 
Decibel is just a value defining ratio of two values. Ratio of 1/1 equals 0dB. So what is 0dB is defined by what is used as a “reference value”.
See: Decibel - Wikipedia
BTW, there isn’t such thing as “dead silence”. And if there were the sound pressure level in such condition would be -∞dB, not 0dB.
Or if you like, the scale is showing you the amount of gain in dB referenced to unity gain (0dB), that is no gain. so therefore -3dB is 3dB gain in a negative sense, hence 3dB less than no gain 0dB (unity)
every 3dB change is around half or double volume and every 6dB change is around half or double amplitude depending on direction.
Hi, Folks!
One thing that’s not mentioned in this discussion is that, “Some of our senses operate in a logarithmic fashion (Weber–Fechner law), which makes logarithmic scales for these input quantities especially appropriate. In particular our sense of hearing perceives equal ratios of frequencies as equal differences in pitch.”
In other words, a logarithmic scale (i.e. decibels), provides a mathematical method for aligning measurements with certain human perceptions, e.g. hearing, vision, touch, etc. It permits a very wide and non-linear range of physical inputs to be reduced to relative terms (hence, the use of the word “ratios”).
As an example, human hearing has a range of approximately 130 decibels from the softest sound that can be detected, 0 dB Sound Pressure Level (SPL), to the point where the intense motion of the air causes physical pain around 130 dB SPL (note the “SPL” qualifier). If I recall correctly, cranking the numbers points up that this is a ratio of 1 to about a trillion from the softest detectable sound to the loudest humans can tolerate. (The air at sea level actually starts going non-linear and “distorting” at about 165 dB SPL.)
As noted by the prior reference to decibels by Jarno to wikipedia, this mathematical device permits measurements that are more easily understood in terms of simplified quantities of numbers.
Hope this helps shed further insight into the usage of decibels.
Read up on logarithmic scales in general, they don’t work at all like the linear scales you usually work with in other fields.