It's simply a ratio, the actual value it's expressed in is the 'Bel', but this is usually too big, so the 'Decibel' is used - this is what the '10' in checkmates equation is for, to convert from Bel to Decibel.
It's commonly used for audio or RF signal applications, mainly because of the 'log' in the equation, this gives it a logarithmic response which makes things simpler.
Because it's just a ratio (and not an absolute value of anything) you need to specify what it's compared to - 0dB if often set as 0.775V, basically line level. So a negative figure is lower than that, and a positive figure is higher.
You should also be aware that dB's can be used for both POWER or VOLTAGE, but they are not the same values!.
It's often said that people who talk about dB's don't know what they are on about 8)