And how does a quartz crystal keep time?
How does a guitar-string or tuning-fork keep its pitch?
Mechanical resonance.
Basically the same thing; a quartz crystal is cut into a shape that mechanically resonates (some are literally cut into an ultra-miniature tuning-fork shape), and uses a bit of electronics to sustain the oscillation forever.
Quartz crystal and other piezo-ceramics have a property that means they change shape very slightly when you apply a voltage across them (you deposit a thin silver plating on two sides) and conversely if you squeeze or strain them they produce a small voltage. This allows electronics to monitor, and feed back and sustain the oscillation.
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