Rogoff defines a central banker as one who has no private incentive schedule and for whom θβ > θ. θβ being the weight the central banker puts on inflation deviations relative to unemployment deviations.
Inflation is lower on average and less variable than it would be if set by a social planner with less conservative preferences. Appointment of a central banker is not the best solution though, because as long as θβ < infinity the inflation bias is still influential. Lower variance of inflation is achieved through higher variance of unemployment.
See Page 145 Drazen