Does anyone actually "understand" what is going on in the schematic above?
If you simplify the diagram (by combining the paralleled capacitors into one, and ignoring the resistor), its function becomes apparent:
In one position, the relay bypasses the capacitor - applying the mains directly to the fan (for full speed). In the other position, the fan is supplied via the series capacitor (which reduces the motor's speed).
When your boiler is operating as an instantaneous water heater, the gas rate will be at the boiler's set maximum. The air supply also has to be at its maximum (full fan speed) to achieve complete combustion. When starting from cold in central heating mode, the gas rate is initially at the maximum (to heat the system up quickly), so the fan has to operate at full speed. Once the set water flow temperature is reached, the modulating gas valve reduces the gas rate to a level sufficient to maintain the flow temperature. At this reduced gas rate, less air is required for combustion. Hence, the fan's speed can be reduced. The benefit of reducing the flow rate through the flue is that it enables the boiler's heat exchanger recover more latent heat energy from the flue gases. Thereby, improving the boiler's energy efficiency rating.
Also, where does the 10K resistor come into this?
In so far as supplying power to the fan, the resistor contributes nothing. The resistor is bypassed in both relay switch positions (that's why I greyed it out in the diagram). The resistor in series with the capacitors does look like a snubber circuit. However, the values of the RC combination gives a time constant of 24.7ms, which is greater than the period of a mains cycle. It would not, therefore, be of much use as a snubber. The resistor is only, effectively, in the power circuit for a brief moment, as the relay switches over. Some tap changers on high power transformers switch in resistors, between taps, to reduce arcing. Perhaps, the resistor's function is something similar or, more likely, it's simply a bleed resistor - connected across the capacitor while the fan is at full speed.
The 275V rating of your class X2 capacitors is the AC rating (RMS, not peak), which should be adequate for use at UK mains voltage. So, for those capacitors to fail prematurely, they must be being exposed to high voltage transients, high temperatures or both. Excessive voltage transients might be generated if the relay is switching its inductive load too slowly or its contacts are chattering. That could be caused by failing electrolytic capacitors in relay coil driver circuit (the relay being energised with a high ripple current, instead of clean DC).