The basic reason is that sound pressures span a WIDE range of orders of magnitude, despite that it may not seem like such.
The faintest sound you can hear(*), at least if your ears are good, is taken by standard to be 20 μPa. And this sets the level for 0 dB. That's micro pascals, by the way, or $10^{-6}$ pascal. The loudest sound you can hear is one where the pressure equals the actual pressure of the atmosphere - again, by standard, taken as 101.325 kPa, exactly (so the actual atm. pressure at your own location may be different). You don't want to hear this sound, though: not only would it destroy your ears, but it'd be effectively like getting hit by a bomb blast - quite easily lethal! (You can, of course, make a pressure wave in air that's even stronger - that's what a bomb does very close in - but you can't really call that "sound" anymore. Actually, even this may be "pushing the envelope" as to whether it's sound.)
Suppose though we tried to use instead the micropascal as our choice unit. Then that level is 101 325 000 000 μPa, against 20 μPa. That's kind of awkward to write. Moreover, using scientific notation, $1.013\ 25 \times 10^{11}\ \mathrm{μPa}$, is ugly, and switching to larger/smaller pressure units by changing the prefix makes the comparisons less clear (there's a sort of guideline that you, generally speaking, should stick to a single unit of a particular size for a given physical quantity throughout a context, even if it may result in large numbers and/or imprecise ones perhaps requiring scientific notation along with more reasonable ones, for just this reason). But writing 0 dB and 194 dB, respectively for lowest and highest sound, is much cleaner. One unit and one reasonably compact number.
Logarithmic scales - and actually, the unit "decibel" isn't just for sound, it is a generic logarithmic measure that can be used for just about anything - are quite standard for dealing with quantities that span many orders of magnitude, even ones that have nothing to do with sound: for example, electronic signals in signal processing circuitry like that used in radio communication, are often measured using dB as well, relative to some other reference level appropriate for them (and also that is not a pressure, but typically a power [rate of energy delivery], or voltage, or something of that sort). Astronomy even uses this to measure the brightness of stars, whether actual or as seen in the sky at distance, quantities which also have similarly-great variation, but there, their unit system is a terrible mess and their logarithmic scale is a weird one that not only does not use base ten but also rates things as higher in "magnitude" when they are fainter, not brighter. I really think they should use dB like everyone else, with suitable reference points, but fat chance to tilt at so much entrenched tradition.
(*) People with highly sensitive ears, such as in some manifestations of autistic spectrum disorders and other disorders with sensory processing modification, seem to report the ability to hear sounds much fainter, like a tiny bug crawling on the wall nearby - but I've never heard of a measurement study done thereupon. 20 μPa is the threshold for an average human, not the lowest possible sound such that no existent human can hear lower. Also, if you have tinnitus (as I do), chances are quite good you can't even hear this low.
