The decibel (symbol dB) is a way of expressing a ratio. It is based on logarithms, and so adding decibels is equivalent to multiplying their corresponding ratios. Decibels can be used to express absolute values by referring them to a reference value.
A common use of decibels is to express ratios of amplitudes. For instance, the amplification (or gain) of an amplifier can be expressed either as the ratio of the output and input amplitudes, or as a certain number of decibels. With a multi-stage amplifier where the gain of each stage is expressed in decibels, the overall gain in decibels is just the sum of the individual stages' gains.
The sound pressure level (SPL) is a unit for expressing the amplitudes of sound waves relative to the threshold of hearing. The SPL system uses units of decibels, and the lower threshold of hearing has a value of 0 dB. An advantage of the SPL as a unit is that it reflects the way loudness is experienced. That is to say, equal increments of SPL are heard as approximately equal increments of loudness.