Chuck called it right - the semi-conductive brush provides interpolation of the output between the discrete steps of the windings. It has to bridge at least two turns at any position, to give a relatively smooth transition between steps. If it didn't, the output would necessarily be discrete steps of voltage, and include "off" (disconnected) states in between, which wouldn't be good. It's a compromise to provide more or less continuous output control, and it does waste some power to heat the brush, and it contributes to wear, besides the mechanical friction. Larger variacs have extra features for better cooling of the brushgear.
The conductivity, abrasiveness, contact force, and shape of the brush have to be just right for best trade-offs between smoothness, power rating, and life. Variacs can be very tricky, but this was all pretty much perfected before any of us were born. Be happy that they work so well at their purpose.
The same sorts of issues arise in other devices where discreteness needs to be handled with smoothness and continuity, like a wirewound pot or rheostat, or the commutator of a motor.
A related, interesting insight can be gained by studying the carbon-pile, a very old-school device.