Part 1: Decibels are just a ratio:

Decibels are a ratio, just a number to multiply by. While decibels are often shown as a negative value, the ratio is always positive. The ratio can be very tiny or huge, but always positive. For example, 3 decibels means about 2x the power, but -3 decibels means half the power. ‘Drop by 3 decibels’ means power is one-half of what it was. Drop by 90dB is -90dB and means power is one-billionth of what it was. One-billionth is tiny, but still positive.

Part 2: “to the power” from math, the logarithmic scale  part of decibel:

A decibel is 1/10th of a bel. A bel means “power times 10 to the power __” so a decibel means “power times 10 to the power __ / 10.” Therefore, every 10 decibels is a change by a factor of 10. 10dB is 10x, 20dB is 100x, 30dB is 1000x, -10dB is one-tenth = 0.1, -20dB is one-hundredth = 0.01, -30dB is one-thousandth = 0.001 and so on. Always positive, but ranges from tiny to huge quickly.

Part 3: the “power from physics” part of decibel:

Where the math ‘power’ is the second ‘power’ in the dB description, the first ‘power’ means decibels are assumed to refer to the ratio of power of whatever it is describing. Therefore, don’t try to make physical sense of what a decibel actually is, just know that it means more or less power from any of a variety of other units that describe actual physical phenomena that produce power. Negative decibels means power has diminished (but is still positive). Positive decibels means more power.

Common Examples

The most common example of decibels is to measure sound level. I don’t know what the power reference is for sound decibels, but there must be one and I know the power of 3dB of sound is half the power of 6dB of sound, which is one-tenth the power of 16dB of sound and so on.

Another common example is signal loss in a cable. Since a cable is not powered, these are always “negative decibels,” and usually written as “signal loss per length wire,” which means multiply by something less than one. 3dB per 100 meters of signal loss really means -3dB / 100m and the signal loses about half its power every 100 meters. If the signal travels through 500 meters, it has lost 15dB, which means about 1/32nd of the original power.