Mr Murray, the brushes are there to take electricity to the middle of the motor, known as the armature. The part which the brushes touch is called the commutator. The commutator has segments which are connected in pairs to the coils on the armature. Around the armature sits the field coils.
In simple terms, it works like this:
When the motor is energised, electricity flows through the field coils and creates a magnetic force. At the same time, electricity flows through the brushes to the commutator, through the coils in the armature, and out again, and this creates a magnetic force too, but one which repels the force from the field coils. Thus, the armature moves because of the repulsion. The segments of the commutator work in pairs, on opposite sides to each other, and as the armature moves, the pairs which were touching the carbon brushes are no longer doing so and the electricity flows to the next pair, which repel the force of the field coils, and so on it goes, turning the armature as it does so.
There was an excellent television broadcast a good deal of years ago, probably before you were born, where a gentleman explained how a vacuum cleaner motor worked and even made a replica motor from a food tin amongst other objects. The motor was crude, but it did work. I cannot remember what the program was, because if I did I would refer you to it as it may be feature on line.
