Apparently you're going to get transformer theory and AC current theory to answer this one question.
AC (alternating current) begins @ 0 volts increases to its maximum positive potential, decreases to 0 again, then swings to its maximum negative potential, and returns again to 0. So, in one complete "cycle" (Hertz is more widely used today) the voltage is at 0, 3 times, with 1 full excursion positive, & 1 full excursion negative. When a graph is made of this cycle, in house current, the graph has a particular shape, and again in house current, this graphic representation is called a "sine wave".
Please check this Wiki page;
http://en.wikipedia.org/wiki/Sine_wave
Voltage DIFFERENTIAL is established with a transformer. A transformer will only pass an AC signal, it has no effect on, and will not pass DC (direct current) which only flows in one direction. At it's simplest, a transformer has two coils of wire, a primary and a secondary, which relate to the input (primary), and the output, (secondary).
In an simple example with house current voltages, suppose we have 100 volts at the wall, but we need 120 volts to run our equipment. If the primary coil of the transformer has 100 turns of wire, then the output would need 120 turns of wire to yield 120 volts output. The mechanical ratio of windings, relates directly to the electrical ratio of the transformer. The 100 turns is a simplified representation, but any physical ratio of windings will always be equal to the electrical ratio produced.
In our example about house voltages, the ratio is 1 to 1.2. So, if our transformer had 1000 windings in the primary, it would need 1200 windings in the secondary to yield the same voltage differential.
Please see this Wiki page on transformers;
http://en.wikipedia.org/wiki/Electrical_transformer
Transformer coils can be tapped any where in the windings. If we put a tap in the secondary windings of our original transformer @ 100 turns, then the voltage out, would be equal to the voltage in, since both coils now have the same number of turns in their windings. This is the principle behind the "variac", one of the coils is tapped in many places, and switching to these other taps alters the ratio of the coils, thereby changing the voltage ratio. In an "AVR", this switching is done well, "automatically".