Washing machine carbon brushes transfer electricity to the armature of the motor. The armature will then spin and the drum will turn via the drive belt. Washing machine carbon brushes are spring loaded in order that they are always touching the motor armature. Once they are worn to the point where contact is no longer possible the washing machine motor will not turn.
Of course there are other components including electronics that are also responsible for motor rotation but worn carbon brushes are one of the most common reason for your washing machine drum to stop turning and spinning.
If your brushes are worn or damaged when you come to use your washing machine it will fill up with water, appear to sit idle for the duration of the wash and spin cycle (because the drum won't turn), and then drain out the water, and when you open the door of the machine to remove your clothes they will still be soaking wet!
You can find further help and advice here relating to other faults that can cause your washing machine drum to stop turning.
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Haimen Hailing Carbon Industry Co., Ltd. , http://www.carbonbrush-hl.com