........It's a simple RC oscillator, using R1 and C5 - if pin 1 is LOW, then pin 2 will be HIGH, and C5 will charge through R1. Eventually the input on pin 1 will become high enough to switch the inverter, and the output will switch LOW - R1 will then discharge C5 until it switches again. This process will repeat continually, creating an oscillator - the output on pin 2 will be a squarewave, and the input on pin 1 will be a rough triangle wave.
The crystal isn't really part of the oscillator, but it's presence will force the oscillator to 'lock' to it's frequency, as long as it's fairly close to begin with.