How does a quartz crystal work?
Quartz is a piezoelectric material, which means that if you mechanically deform it, it develops charges on its surface. Similarly, if you place charges on its surface, it causes mechanical stress in the crystal. The way a quartz crystal benefits a circuit is that mechanically the crystal acts much like a tuning fork, with a natural resonant frequency, and the piezoelectric property allows that to be coupled into an electronic circuit. Since the resonant frequency is mainly determined by the physical size and shape of the quartz, you get a frequency reference that is much less sensitive to temperature than you would get using just LC circuits.