A crystal oscillator is an oscillator circuit that uses a quartz crystal to create a stable frequency. The crystal vibrates at a predictable rate when used in the right circuit.
Where crystal oscillators are used
They are used in watches, clocks, radios, computers, microcontrollers, communication devices, and anything that needs accurate timing.
Why crystals are stable
A quartz crystal has a physical resonance that helps keep the frequency steady. That makes it more accurate than many simple resistor-capacitor timing circuits. It is a specific kind of oscillator.
When electronics need a reliable heartbeat, a crystal oscillator is a common answer.