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I reckon it's a low-pass filter to kill fast transients when the triac opens the circuit (agreeing with Phasor)
Such 'snubber' circuits are fairly common across sensitive circuit mains supplies. The triac will only cope with
maybe 400v peak (on 120v mains) and noisy mains supplies can fry them without this protection.
Or ... :?
Do I remember something about inductive loads causing problems with triac triggering - the phase-shifted
current preventing the triac from ceasing conduction; once you fire the triac it will 'flywheel' and you can't
shut it off.
If this is the case then the cap gives an alternative current path while the triac shuts down.
I favour the first explanation though :!: (so that last bit must be a load of @$%^)