Piezo speakers have a high impedance hence they require a relative higher driver Voltage. 2 AAA batteries may supply about 1V RMS at best. That is why you need a step up transformer which in your case happens to be an autotransformer. The primary coil is A-C, the secondary coil is B-C. Since this is an auto transformer the secondary coil includes the primary coil in series, as a result the primary Voltage adds to the secondary Voltage.
The number of turns is directly proportional to the Voltage across the coil. For instance if the primary coil is 3 turns and the secondary coil is 30 turns you will get in case of 1 V RMS input 10+1 Volts = 11 Volts RMS.
Of course the previously mentioned posts about the ringing and self resonant of the Piezo element are all true.