The Rectifier is an electronic device, which converts an AC waveform(Usually a Bi-directional waveform with Zero Average value) to a Pulsating DC waveform (Uni-directional waveform with Nonzero Average value).
As AC wave (Sinusoidal) has two half cycles, namely -
Positive Half cycle & Negative Half cycle
If a Rectifier does it's operation only in one half of the cycles, it is known as Half Wave Rectifier.
Similarly, If a Rectifier does it's operation in both the half cycles, it is known as Full Wave Rectifier.