I don't know why my check engine light is on... Audi 1997 A4 Quattro (see details)?

Not the only reason, but one possible and most simple is that the gas cap may be loose, or the engine was left running while it Was being refueled.
Hopefully this is the cause. The solution is to check the gas cap make sure it is tight, disconnect the battery for a couple minutes, hook it back up and see what happens. If that doesn't fix it, the you have eliminated the cheapest solution first.

ADDED:: Techgl may be right if I'm not..

Maybe a coolant temp sensor. Very likely

The On-Board Diagnosis (OBD II) is required to monitor engine temperature as part of the emissions monitoring. when a problem is detected that can lead to excessive emissions then by law the OBD II system has to turn on th check engine light.

The problem that is being detected on your car is that the engine temperature is running higher than it should. Hot engines produce more tailpipe emissions of an exhaust gas known as NOx (Oxides of Nitrogen). So the check engine light is on because the engine is running hotter than it should and more than likely producing excessive emissions.

The original term for this particular diagnosis was "thermostat monitoring" where the on-board diagnosis system monitored the opening and closing of the engine thermostat to regulate engine temperature. Different manufacturers use different terminology but essentially the check engine light is telling you that the engine thermostat isn't regulating the engine temperature as it should.

the problem is most likely with the thermostat for the cooling system but the conditon can also be caused by a low coolant level or restrictions in the cooling system. The odds say its the thermostat that's bad

hope that helps