A vocoder is a sound effect that can make a human voice sound synthetic. It is often used to speak like a robot, with a metallic and
monotonous voice.
To put it simple: whenever you speak, your voice consists of two components. The first component is your basic voice type, produced by your vocal chords. It varies in pitch but remains nearly constant in type and is quite unique. That's why you can distinguish between persons when you hear their voices. The second component is how you
modulate the basic voice.
Modulation means that you dynamically
amplify and attenuate frequencies. This is done by the mouth and tongue when you speak.
The benefit of doing this is, you can make the carrier speak or sing. As a side effect, the formant's voice type is absolutely irrelevant to the output so everybody (even those with an ugly voice) can create cool and futuristic samples.
If you want to hear good examples of it's usage, listen to a few songs from
Zapp & Roger/Roger
Troutman.