The motor on your vintage Singer has two of those brushes, and their purpose is to conduct electricity from wires which don’t move to a bit of the motor which does, in order that the motor might turn and drive your sewing machine.
That particular moving bit of the motor is called the commutator, it’s a kind of rotary switch made of copper segments, and it lives on one end of a shaft at the other end of which is the little pulley with your drive belt on it.
Those springs push the carbon against the commutator, which is whizzing round at a fair old rate when you step on the go-faster pedal, so not surprisingly the carbon very slowly wears away.
Top carbon is new the bottom two are worn away! I am off to check my machine!
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