A capacitor is an electronic component - here's a picture of a 0.68 Micro Farad capacitor... 0.68uf
http://ampbuildersparts.com/store/images/mini-Black%20cat.JPG
It will probably be a part of the printed circuit board of your boiler. Capacitors are used in electronic circuits to remove high transient voltages, to smooth rectified DC and - most probably in the case of your circuit-board - as part of a timing circuit.
The circuit symbol for a capacitor is not unlike like this -||-
Some capacitors are polarized meaning that they must be inserted into a circuit the correct way round - you can see a line around the can of the capacitor in the picture indicating that it's polarized.
The unit of capacitance is the Farad but a 1 Farad capacitor would be quite big - thay are usually sold and used in the MicroFarad range.
Capacitors also have a voltage rating indicating the maximum voltage they can withstand. Many also have a temperature rating - perhaps 85 degrees C or 105 degrees etc.
Electrolytic capacitors tend to age prematurely with time and heat - boilers tend to be warm - capacitors in boilers tend to fail.
You do not mention the make or model of your boiler.
If your boiler fires up to make hot water but not to heat your radiators the fault is unlikely to be in the boiler but in part of the external controls etc. Combination (combi) boilers do care but most other boilers have no idea why they are being asked to fire up - hot water or central heating - it makes no difference to them.
Good luck...
Peccavi
May 2010