The four rings of Audi represent the four companies of the Auto-Union consortium of 1932 - DKW, Horch, Wanderer, and Audi. After the war the Audi name - which is Latin for "Hear!" - disappeared, but was revived in 1965, using the four rings as a logo.

Also, the name is sort of a pun on 'hoerch', German for 'hear', name of one of the founders.