Peter Frampton and his "talk box"

YouTubel link.

I must have heard this song a hundred times without understanding how the effect was achieved.

A talk box is usually an effects pedal that sits on the floor and contains a speaker attached with an airtight connection to a plastic tube...

When activated, the sound from the amplifier is reproduced by the speaker in the talkbox and directed through the tube into the performer's mouth. The shape of the mouth filters the sound, with the modified sound being picked up by the microphone. The shape of the mouth changes the harmonic content of the sound in the same way it affects the harmonic content generated by the vocal folds when speaking. The performer can vary the shape of the mouth and position of the tongue, changing the sound of the instrument being reproduced by the talkbox speaker. The performer can mouth words, with the resulting effect sounding as though the instrument is speaking. This "shaped" sound exits the performer's mouth, and when it enters a microphone, an instrument/voice hybrid is heard. 

Text from Wikipedia, which also has a history of the development of the talk box and its use by other musicians.