Definition
A unit for measuring the strength of a sound or the relative size of a signal. Unlike an ordinary ruler, where the number goes up by the same 1 each step, every 10 steps up the decibel scale means the actual sound energy jumps 10 times higher.
Sound went up by 10, but the energy went up 10 times?
The rulers we use every day grow evenly: 1 cm, 2 cm, and so on. But in the world of sound, decibels follow a completely different rule. When the decibel number goes up by 10, the sound energy becomes 10 times stronger. When it goes up by 20, it is not 20 times stronger. It is a full 100 times.
Say a quiet library is 40 dB and normal conversation is 60 dB. The gap looks like just 20 dB. But the real energy the sound carries (its intensity) means conversation is 100 times stronger than the library. An 80 dB subway is carrying 10,000 times the energy of the library.
When a small bump in the number means a huge jump in real power, math calls it a logarithmic scale. Sound energy swings across such a gigantic range that writing it out would take a string of dozens of zeros. So people invented the decibel, a clever compressed scale.
The clever secret of how your ears hear
Why do sound meters bother with such a tricky compressed scale? One reason is that the range of sound energy is far too wide. The other is that this scale is a lot like the way human ears sense sound. Your ears only say 'that got about twice as loud' once the sound energy has grown about 10 times.
Imagine if your ears took in sound energy at face value. Ears delicate enough to catch the faint rustle of a leaf would be wrecked the moment they heard a fairly loud clap of thunder, because of all that energy.
When a sound is very quiet, your ears pick up tiny changes sharply. When a sound gets huge, they react more dully. That is how you can hear a wide range of sounds. But just because a sound doesn't feel loud doesn't mean it is easy on your ears. The decibel was originally made for handling telephone signals, but it also matches the way ears sense things, so it is widely used to describe sound.
To be a little more precise
The most common mix-up about decibels is what 0 dB means. Just as 0 degrees is not the total absence of heat, 0 dB is not complete silence.
0 dB is simply the reference point: roughly the quietest sound a healthy person can barely hear. In other words, 0 dB means 'as loud as that barely audible reference sound,' not 'zero sound energy.' An animal with very sharp hearing can easily pick up sounds even quieter than 0 dB, like -5 dB or -10 dB.
Also, the decibel (dB) is named after Alexander Graham Bell, the inventor of the telephone, with 'deci,' meaning one tenth, added in front. It started out not as a way to measure an absolute amount of sound, but as a way to compare the ratio between two signals.
Common misconceptions
0 dB means there is no sound at all, perfect silence.
0 dB is a reference point set at the quietest sound people can hear (the hearing threshold). In reality, sounds with negative decibel values, below 0 dB, exist too.
Where you meet it
Leaves rustling in a quiet forest are about 20 dB, and a quiet residential street is about 40 dB.
Earbuds turned up to full volume can reach 100 dB, which carries 10,000 times the actual sound energy of everyday conversation (60 dB).
In one sentence
The decibel neatly compresses sound energy, which explodes in size, to match the way people sense sound.