That isn't always true, but we can get to that later.
Here is a diagram showing the different waveforms from half and full wave rectifiers.
http://dl.dropbox.com/u/4222062/rectifiers.PNG
If you omitted the diodes shown in grey, you would only get half wave rectification. You can follow the path of current along the red and blue lines.
Notice that full wave rectified output has a higher average voltage because it is supplying voltage for a greater proportion of the time. (You can picture the tops of the waveforms above the average lines being clipped off and put in the space between the waveforms below the average line. When this produces a constant level, you can call this the average voltage.)
Half wave and full wave rectified outputs both produce the same PEAK output, though, and they are usually used with a large capacitor across the output. This will charge up to the peak value and give the same output for both types of rectifier.
Even then, though, the full wave rectifier will perform better on load because it gives pulses of charge to the capacitor more often.