Why is everything in audio measured in dB?
Short answer: Because the ear measures things in dB.
The decibel is nothing more than a ratio between two numbers. (The unit was originally just a bel, but for audio it was more convenient to use tenths of a bel, hence the SI 'deci' prefix) Mathematically, the number of decibels between two numbers is (20 * log10(N1/N2)). It's sufficient to know that when you add dB, you multiply numbers. In particular, 20dB multiplies your value by 10, and 6.02dB (most people just say 6) will double it. Negative dB means dividing.
Why is this important? Well, it establishes that dB is a logarithmic scale, in which the numbers get closer together the higher they get.
So let's split the question into two. First, why is signal level measured in dB? The ear, like everything in the body, doesn't care so much about how loud something is, but rather how much louder it is than something else. Your hearing sensitivity goes up when it's quiet so you can distinguish quiet sounds, but the sensitivity goes down when it's loud to protect your hearing. On a regular linear scale, all of the interesting volumes (whisper, talking, even a car horn) are bunched up at the bottom. This is logarithmic behavior.
Why is frequency measured in dB? Okay, you caught me. Frequency is measured in Hz. But we don't think in Hz, do we? As any musician should be able to tell you, humans hear in octaves, not Hertz. And an octave is exactly 6.02dB (a factor of 2). The difference between 17220Hz and 17260Hz is almost unnoticable to most ears, but the difference between 40Hz and 80Hz is a whole octave. Since the difference is again proportional to the scale, it makes sense to plot frequency on a logarithmic scale.
This has the interesting effect that the most useful way to plot sounds meant for human ears is on a 10x10 grid. On the horizontal axis, you plot ten octaves (log2(20000Hz / 20Hz) == 9.97 octaves), and on the vertical axis, you can plot ten Bels, the difference between the threshhold of hearing (about 10dBSPL) and the threshhold of pain (about 110dBSPL). The human ear measures sounds fairly uniformly all over this grid. If you tried to plot the same thing linearly, all of your interesting data points would be crowded down in the lower left corner.
So why are things measured in dB? Because in both frequency and amplitude, humans hear logarithmically. And the dB is our unit for measuring logarithmic scales.