I assume you mean in a full-wave rectified power supply such as <a href="http://www.circuitstoday.com/wp-content/uploads/2009/08/centre-tap-full-wave-rectifier.jpg">THIS</a>.<br />The centre tap would not necessarily be to earth, but to the 0V rail of the supply.<br />This sets a reference point and the voltage on the other two outputs swing above and below this - when one end is at a maximum (say 10V) the other is at a minimum (-10V) relative to the centre tap. <br />With the diodes in the circuit, as each side swings high, the diode conducts and allows current to flow to the positive voltage rail (again, relative to the 0V centre tap). When each end is at a minimum, the diode is reverse biassed so does not conduct. Thus, only positive cycles reach the output. <br />You would normally have a capacitor at the output to smooth the voltage.<br />
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Exactly. Basically, it's being used as two transformers at once, one hooked up backward from the other and with their centers tied together. The center-tapped solution's more compact and cheaper to manufacture than two seperate transformers would be.