They are circuits that convert AC to DC.
A half wave rectifier only converts the positive or only the negative part of the AC sine wave to DC. This means that the DC voltage output is pulsating.
This can be achieved with just a diode.
A full wave rectifier can convert the AC sine wave to a rippled DC voltage. This means that the DC voltage will be all the same sign or zero.
This can be done with either a center tapped transformer circuit or a bridge rectifier.
In order to smooth out the DC output, one can add filters. The easiest way to do this is to add a capacitor.
Center tapped full wave rectifier
Bridge full wave rectifier