AUDI is the latin word for Horch.
August Horch founded his company "August Horch Automobil Werke Gmbh, Zwickau". Some years later he lost "his" company to other persons and so he founded an new company that called AUDI.

The letters NSU stands for "Neckarsulmer Sickmaschienen Union" that means Neckarsulms knittingmachine company. This company is founded by Christian Schmidt and Heinrich Stoll in 1873. Since 1892 the meaning of the letters changed into the short version of the city-name of the NSU headquater: Neckarsulm.
Often the people say Neckars-ulm, because they think Neckarsulm has something to do with the famouse city Ulm or New-Ulm. But thats not right. The name Neckarsulm comes from the two rivers Neckar and SUlm, that combined in Neckarsulm.

Joe
PS: Sorry for bad english....