Step-by-step explanation:
Think of brushes as a sliding contact.
In an alternator the brushes provide power to the field coil which is physically mounted on the rotating shaft. They provide this direct current through two slip rings.
By controlling the power flow to the field, the power output of the alternator can be controlled. A regulator circuit is used to control the field so that the output voltage is maintained to about 13.5 to 14.5 VDC.
FUN FACT: Many brush holders have a small holes near the brush exit. When you assemble the alternator you physically push the brushes all the way into their holder and then thread a small wire through these hole. After the alternator is assembled you can pull the wire out and the brushes will snap into position.