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There are two kinds of crystal oscillators. One operates at what is called the "series resonance" of the crystal. This resonance is the frequency at which the (AC) impedance between the pins of the crystal is almost zero. The frequency is independent of how much capacitance happens to be in parallel with the crystal - its inside the oscillator and part of the circuit board, etc. But, even frequency that the oscillator runs at.

The other kind of oscillator oscillates at "parallel resonance"of the crystal. At this frequency, the impedance from pin to pin of the crystal is almost infinite. This frequency depends on how much capacitance is connected in parallel with the crystal. This parallel capacitance is called "load capacitance". Generic signal-inverter oscillator is this kind of oscillator.

The common oscillator connection is for the crystal to be connected from the inverter output to the input. And, there is a capacitor at each end of the crystal to ground. The NET load capacitance is SERIES equivalent value of those two capacitors.PLUS stray capacitance from the circuit board and the guts of the oscillator. Suppose that the crystal is rated for 22pF load capacitance. The stray capacitance is about 7pF. So, that leave 15pF to be made up from discrete external capacitors. If the external capacitors are equal, then their equivalent is half of their individual value. Thus, in this case, we would want a pair of 30pF capacitors.

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Q: Why use capacitors with crystal oscillator?
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