Decibel

A decibel (or dB) measures ratios of power or intensity. It expresses them as an exponential function. One bel is a power ratio of 10:1, and is divided into ten decibels. An increase of three decibels is approximately a doubling of power. Decibels are often used in measuring telecommunication signals. With electric audio signals, there are several decibel units, relative to several bases. For example, dBm is relative to one milliwatt.
It's been said that the smallest difference humans can hear is 0 dB and is related to the Absolute threshold of hearing, although this is very subjective at best.
History.
The bel unit was named after Alexander Graham Bell. This unit was so rough that it is more typical to use the decibel, which is one bel divided by ten. Before bels, there was the Transmission Unit (TU).
Examples and Protection.
Often, decibels are used to say how loud a sound is relative to the threshold of hearing. The decibel is not an SI unit. The table here uses dBSPL as units of sound to indicate consensus on hearing protection. Some examples of sounds are:
Hearing protection can also be used to shield from ear damage. This table gives some safe limits for the level of sound so that the ears are not damaged.