Let's see how much of my high school physics I remember...
Although the term originates from the unit of a "bel", named for Alexander Graham Bell and used to measure sound pressure level, dB in this case isn't a unit, but a ratio, used because it's a logarithmic scale, and so easier to express large factors of change. When dealing with units like power, every 3dB represents a doubling or halving of power, and every 10dB represents a ten-fold change. A 6dB change would represent a four-fold change, 9dB is eight-fold; a 100-fold change would be 20dB, 1000-fold is 30dB, and so on. When talking about units like voltage and current, those figures are doubled (6dB = double/half, 20dB = 10x change). This works because power = voltage times current.
This is especially useful when dealing with human senses, because we don't perceive sensory input linearly. With sound, for example, a 3dB increase, or doubling, in volume is about the lowest change readily detectable by the average human hearing, whereas a 10dB increase is generally heard as "twice as loud".
When it comes to exposure gain, the same math applies: you can double the actual output signal, but it won't make the image twice as bright; instead, it requires a ten-fold boost in level to double the image brightness. Generally the "max" setting is designated 0dB, and attenuation levels below that are marked at negative dB levels... so you can either have -6, -12, -18, -24, -30... or 1/2, 1/4, 1/8, 1/16, 1/32, etc. Measuring this in dB is not only more efficient, it takes up less room on the label :)
There's more detail in this Wikipedia article.