Mechanism of working of full wave rectifier using center tapped transformer

The only purpose for the center tap is to eliminate the need for the two extra diodes (total of four diodes) one would need in a full wave bridge to do the same thing (rectify each half of the wave so that a positive pulse is available twice per single incoming wave). Specifically, full wave rectification means the positive half of the incoming wave is available as positive voltage at the output, and the negative half of the incoming wave is also available as positive voltage at the output--so you get two positive pulses for each single incoming wave.

The center tap helps because it makes it possible to rectify each half of the incoming wave with a single diode. If you consider the center tap as the common ground (place the black lead of a voltmeter on it), you'll see that the two other secondary leads take turns going positive, first one then the other for a single input wave. So a diode on each of those leads produces a positive pulse, and you get positive pulses twice for each single incoming wave, and so you have full wave rectification.