The capacitor stores electricity much like a battery but can be charged and discharged much quicker. On microwaves the capacitor stores very high voltage and can be dangerous. When you unplug the microwave the capacitor should discharge itself but if it doesn’t you could get shocked by the high voltage. At the bottom of that page right after step #13 you will see a picture of the capacitor if you short the leads of the capacitor to ground with an insulated screwdriver or insulated wire you will know the capacitor is discharged.
Note that I have been working on microwaves for over 15 years and have never seen one have voltage on it with the microwave unplugged but I know it is possible and you should be aware of the possibility.