A quartz crystal ground to a thin plate is equivalent to an oscillating circuit with a very high Q factor (of the order of thousands). It is used with an amplifier, which supplies positive feedback, from its output, to the crystal in the input circuit. A fluctation in output current initiates mechanical oscillation in the crystal. The crystal is subject to a mechanical flexure or dimensional change, so generating a varying piezo-electric charge and consequent varying voltage. This becomes the input to the amplifier.
A quartz crystal may be cut at various angles wrt the axes of the crystal using a diamond saw. The plates may be cut to give a particular mode of vibration, to give highest output for a given frequency, or to have a low temperature coefficient of frequency change.
The crystal oscillator has a much more stable frequency than an LC circuit, so is used in radio transmitters, receivers, and timing circuits for equipment such as computers.
