As a filter.
A filter is a three terminal network, one pin ground, one input and one output. The input and output are interchangeable for purposes of signal flow (a filter always works the same in both directions), but their impedances can differ; a symmetrical filter of course has identical impedances and it doesn't matter at all.
The kind of filter used is a bandpass, so that a signal applied on one side is strongly attenuated except for a peak at the desired frequency. Crystals give a very narrow, sharp, well defined frequency, making them great for precision timing and filtering.
The equivalent circuit of a crystal is a series resonant network, with some capacitance in parallel. A series resonant circuit has minimum impedance at resonance. If we put the crystal in series (from input to output), we get transmission through the filter, at resonance. That's good. But we also need some impedance to work against, otherwise plenty of signal will be let through away from resonance. It's not enough to have an impedance that varies: we need an impedance divider. So we add loading capacitors, from input to ground, and output to ground. This transforms the crystal into an equivalent parallel resonant circuit (as if input and output were tied and the crystal were parallel resonant to ground), giving a typical bandpass characteristic.
What impedance is the crystal filter? Typically low kohms (for ~MHz range crystals).
If the oscillator has a logic level output, there will be a series resistor connected to the filter, which terminates the filter and drives it with adequate power (you don't want to overexcite the crystal -- it can shake itself to bits!).
If the oscillator has a linear or current limited output, it will connect directly, and it doesn't look like anything special is going on (you have two pins, OSC1 and OSC2, and a crystal and two caps between them), but it's still the same input-output filtering scheme.
The impedance is basically the reactance of the loading capacitors, give or take an error factor. Thus a crystal that takes 20pF at 50MHz is a very low impedance, while one that takes 4pF at 32.768kHz is a very high impedance indeed (100s kohm). The latter is very useful for low power applications (it consumes very little drive current, and power), but be careful that it's also sensitive to contamination (say if there's conductive flux residue on the board).
The one difference is if there's a single pin oscillator, which internally is a negative resistance circuit, which resonates with a crystal and one or no capacitors (in its parallel resonant mode, slightly off from rated frequency).
Tim
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