The Motronic system (also called the digital motor electronics, or DME) is the heart and soul of your vehicle's engine. Ignition timing and fuel delivery are controlled by a digital map recorded within the main engine management (DME) computer. The computer takes input from a variety of sensors on the engine-- temperature, altitude (ambient air pressure), crank angle, throttle position, exhaust gas oxygen (mixture), ambient air temperature, and mass airflow--and adjusts engine functions accordingly. The DME is programmed by the factory with a "maps" of certain performance parameters, mostly conservative, so the engine will react well under a host of varying conditions.
Various glitches can show up sometimes due to the ever-increasing complexity of modern DME systems. These systems have many variables that constantly adjust based upon a variety of inputs from the engine as well as the way you drive. Essentially, the computer learns how to work. Sometimes it can lead to trouble. This can sometimes be remedied by updating or "reloading" the DME with the latest version of the software. The downside is that the procedure must be done with the factory Audi computer and can take hours to complete.
Updating the DME with aftermarket software can sometimes result in surprising power gains. Aftermarket suppliers offer different maps that can be downloaded into the vehicle with a laptop via the OBD2 connector. The maps usually do things like advance the ignition timing or spark duration for added power. Installing software is usually an easy process with little to no change in the vehicle's reliability. In most cases, installing software requires you to use premium fuel. The octane requirement can usually be factored into the software for places like California with lower octane premium fuel (91 octane).
Major changes to the engine (including different camshafts, head work, etc.) will require an updated map to take full advantage of these modifications. Failure to update the Motronic system when significantly altering your engine may actually result in decreased performance, and possibly engine damage as the original system is finely tuned to supply the correct timing and fuel injection values for a stock engine configuration. To gain the maximum benefit from engine modifications, you'll need to take the car to a specialist who can perform real time modifications while "talking" to the DME via computer interface.
It is important that you research the supplier before installing aftermarket software. Many times, you'll see products on eBay with exuberant claims of horsepower and the like. A real tuner will be more than happy to talk about the entire process, as well as provide different options for what you'd like to do. Keep in mind that performance software is typically expensive and requires time to get things working perfectly. Simply put, speed costs money. How fast do you want to go?
The OBD2 port (green arrow) located under the dashboard is used to communicate with the vehicle's DME, either to scan for fault codes, update the DME or install performance software.