If you center tap a transformer, it divides the voltage on the winding in half. The center tap lead then becomes a "neutral" line with 0 volts.
For example, let's say you have a step-down transformer that supplies 12 volts, and the secondary winding is center tapped. The transformer steps down 120 volts from a wall outlet to 12 volts. If the secondary winding is center tapped, you will have 3 wires...with 6 Volts - 0 Volts - 6 Volts. From one of the outer wires to the center tap, there will be 6 volts. Across both outer wires, there will be a total of 12 volts.
I have experimented with electricity (including high voltage) for over 10 years. I work with all sorts of transformers, including ones that are center-tapped and end-point grounded. I've also taken classes on alternating current circuits.