I think the point is that with only 3 chords, you can provide a harmony for every note in the scale - i.e. no matter what melody note is playing, at least one of the 3 chords can be played which also contains that note.
The E Major scale is:
E, F#, G#, A, B, C#, D#
The corresponding '3 chords' are:
I chord: E Major (notes 1, 3 & 5): E, G#, B
IV chord: A Major (notes 4, 6 & 1): A, C#, E
V chord: B Major (notes 5, 7 & 2): B, D#, F#
Hopefully you can see that each note in the scale appears at least once somewhere in the above 3 chords.