Basically electronic oscillators rely on a very small piece of quartz crystal that is cut in just the right shape. Quartz has a phenomena called piezoelectricity, where if you apply an electric field, it deflects slightly. Conversely, if you deflect it, it creates a small electric potential. A properly shaped quartz, when exposed to some circuitry (oscillator circuitry; positive feedback), it will resonant at its natural frequency, not unlike how a tuning fork resonates at its natural frequency.

Since the crystal is literally vibrating inside the metal can it's packaged in, the atmosphere around the crystal influences the natural frequency. Helium will make it vibrate it faster, since it presents less air resistance to the crystal.