It's a (to some extent religious) system, which claims, that all chords can be rooted back to only three chords. This system was intensively promoted by German musicologist Hugo Riemann (1849 - 1919)
tonica - triad on the 1st note of the scale (step I of the scale)
subdominant - triad a fifth below the tonica (step 4 of the scale)
dominant - triad a fifth above tonica (step 5 of the scale)
Because there are often chords on the other steps of the scale as well, they are linked to the main functions as "parallel" or "mediant" chords.