I will not enter on details about the Quattro name nor its origins (soon there will be a HISTORY article just for that) but what many people do not know is that not all Audi models are equiped with the "true" Quattro system. Also for more detailed information I placed at the end of the article some links to a more extensive analysis of the Quattro system.
Like you see on the video below the Quattro principle is based on a center diff AKA TORSEN that splits torque coming from the gearbox to the front and rear (most Quattros have an almost 50:50 split but always with a rearward bias with the exception of the Audi R8 that puts even more torque to the rear wheels from the get go, up to 85%). The torque split front-rear is done mechanically altough with the latest generation of Quattro more sensors where added and there is also a distribution of torque left-right and this all putted together can be refered as torque vectoring.
Audi Quattro Torsen system explained
If that principle is valid for longitudinal mount engine models, but for transversal mounted engine models (A2, A3, TT and even other VAG brand models) Audi uses a different system called Haldex (see video below). Its main operation mode is to have 100% torque on the front wheels and when sensors detect the front wheels are slipping, an hydraulic clutch is used to send up to 50% power to the rear wheels.
Audi Quattro Haldex system explained
I would not say that the Quattro (Torsen or Haldex variants) is the best but I can assure it is second to none. Here is a video of Quattro vs other systems.
Quattro vs Others
Here are more links with an more detailed article about Quattro and a video that goes trough and explaing the various system of 4 wheel drive with their advantages and disadvantages. If you like this article please bump. I fyou do not like please comment and let me know why and what you think could improve.