Pythagoras calls three the perfect number, expressive of “beginning, middle, and end,” wherefore he makes it a symbol of Deity. The world was supposed to be under the rule of three gods, viz. Jupiter (heaven), Neptune (sea), and Pluto (Hades). Jove is represented with three-forked lightning, Neptune with a trident, and Pluto with a three-headed dog. The Fates are three, the Furies three, the Graces three, the Harpies three, the Sibylline books three; the fountain from which Hylas drew water was presided over by three nymphs, and the Muses were three times three; the pythoness sat on a tripod. Man is three-fold (body, soul, and spirit); the world is three-fold (earth, sea, and air); the enemies of man are three-fold (the world, the flesh, and the devil); the Christian graces are three-fold (Faith, Hope, and Charity); the kingdoms of Nature are threefold (mineral, vegetable, and animal); the cardinal colours are three in number (red, yellow, and blue), etc. (See Nine, which is three times three.)
Even the Bible consists of the Old Testament, the New Testament, and the Apocrypha. Our laws have to pass the Commons,-Lords, and Crown.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Three from Fact Monster: