In the construction of a full wave rectifier, why is there centre tapped secondary winding in the transformer? OR What's the role of centre-tapped transformer in a full wave rectifier?
Think of the centre tap as a 0V reference; in fact it is usually the ground point on the low voltage side. Then you have two windings, supplying AC in opposite phases. Each winding supplies a half wave rectifier (one positive pulse per cycle), the result is a full wave rectifier (two positive pulses per cycle).
It is slightly more efficient than a single winding and bridge rectifier, because there is only one diode drop between the AC and DC supplies.
But wait - there's more! During the "other" half of the cycle, when a winding isn't providing a positive pulse, it can supply a negative pulse via another diode to provide a negative supply of the same voltage.
So it is a particularly convenient way of supplying +12/-12V (or other voltages) to power analog circuitry.
Apart from the other reasons, as only two diodes are required it can be cheaper than a single winding and diode bridge.