The definition of dB is pretty straightforward, but what makes it confusing is the many variants of dB measurements, based on differing reference points (example: dBm, which is dB relative to 1 milliwatt). By itself, dB is just a ratio of two power levels, or in some cases, of two voltages, using dB = 10 log(P2/P1), or 20 log (V2/V1).
So, a doubling of power is +3 dB, 10 times the power is +10 dB, 100 times the power is +20 dB, 1000 times the power is +30 dB, etc. Going the other way, halving of power is -3 dB, 1/10th power is -10 dB, 1/100th power is -20 dB, etc.
(For voltages, doubling of voltage is +6 dB, 10 times the voltage is +20 dB. This is consistent, because doubling the voltage into a constant load results in 4 times the power, since W=V^2/R. Thus, +6 dB is double the voltage, OR, 4 times the power, while +20 dB is 10 times the voltage, OR 100 times the power. Note that all of this only works out if the load is the same. From now on I will only talk about power dB.)
You sometimes hear about SPL dB, or Sound Pressure Levels expressed in dB. This is a measure of how loud something sounds, and is relative to a reference level of 0 dB-SPL that is supposed to be the minimum threshhold of audibility for a typical human being. Speaker sensitivity is often expressed as the SPL generated by a reference input, which is, if I remember right, 1W into an assumed 8 ohm load, which corresponds to 2.83 Volts. (2.83 squared, divided by 8, equals 1 W). Even though speaker impedance varies all over the map, the convention is to apply 2.83 volts (usually at 1 kHz), even if the actual impedance is such that it works out to more or less than 1 Watt. Typical speaker sensitivity usually ranges from the mid 80's (e.g. an inefficient, small acoustic suspension speaker) to as much as 100 or so (e.g. a horn-loaded speaker), with "typical" being in the high 80's or low 90's. Note that if you measure an SPL of 90 dB-SPL with a nominal 1 W input, 100W would give you 110 dB SPL. (There are scales that relate SPL to everyday experience - the threshhold of pain is something like 130 dB-SPL, whereas a fairly quiet room is something like 30 dB-SPL.) Using a dB logarithmic scale for perceived loudness makes sense, since human hearing does seem to perceive multiples of power as providing linear increases in perceived loudness.
Unlke SPL, the dB reading of a receiver's volume knob is referenced to an totally arbitrary 0 dB level. You'd think that this might be set to be equal to the rated power of the receiver into 8 ohms, and in fact some receivers might follow this convention, but I think that most set the 0 dB point to be at some lower power level. Another "logical" choice is to make it close to the 1W point. Sometimes a receiver review will state what power level into 8 ohms the 0 dB volume setting corresponds to, or else they will state what volume setting produced 1W into 8 ohms. Sometimes this varies by the input selected, due to the pre-amp and processor circuitry having varying anmounts of gain, so it can get complicated. It is also true that you can play games by setting the 0 dB point at an even higher power level, possibly higher than can be actually obtained, just so that the volume at any given numerical setting will be louder than what a competitor produces, thus crreating the illusion of more power.
They could have just as easily set the 0 dB point at some minimal volume level, and then used positive dB numbers as the volume increases - it's all relative. But, volume knobs are (historically, in the analog domain, anyway) basically attenuators, so it was typical to define 0 dB as no attenuation (maximum volume), and then use negative dB for more attenuation (less volume). (In the end, it's like Spinal Tap's amps, that "go to 11".)
It is always surprising to me, to realize how little power is being delivered to the speakers during normal listening. I have a Yamaha RX-V750 (100W x7). In a review in Sound and Vision, they recorded the volume settings, when outputting 1W into 8 ohms with various types of inputs.
For Dolby Digital input, 1W into all channels occurred at a volume setting of -7.5 dB. Using the analog multi-channel inputs, the volume setting to get 1W at all outputs was -2.5 dB. For two-channel stereo it was -3 dB.
My normal listening is usually in the range of -30 to -20 (volume setting), and sometimes as high as -15. This is just fractions of a watt, at least for a steady-state tone.
