A rectifier is a simple device used for creating a DC source from an AC source. The figure below demonstrates a simple half-wave rectifier.
Since the current only flows one way through the resistor the voltage drop can never be negative. The capacitor serves merely as an extra voltage source to even out the sine wave The figure below demonstrates the resulting voltage VS.
The term half-wave refers to the fact that in the absence of the capacitor, a voltage exists only during the time when the primary source is positive. One can make a steadier source with a full-wave rectifier as shown below.
For the full-wave rectifier the current flows from left to right through the resistor for all parts of the AC cycle. This results in a positive voltage at all times as shown in the figure below. The addition of capacitors would smooth out the resulting DC current even further.