Back to the original question (and this just happened on my '00 Civic)
The light is telling you that the car has registered a fault in the emissions system. It put a trouble code in the computer that the technician can read.
On one hand, it could have just been a "hiccup", in which case the light will come on, but nothing is really wrong. You can reset the ECU if you want to see if it was just a hiccup and not an actual problem. One way to reset the ECU is to simply disconnect the negative battery cable for a few minutes. BE SURE YOU KNOW YOUR RADIO SECURITY CODE BEFORE YOU DO THIS. When you connect the battery back, you will have to input this code to make the radio work again (it's a security feature).
If, after resetting the ECU, the light goes off and stays off, it was probably just a gremlin in your system
If it remains on, there may indeed be a problem with your emissions control system. There are (typically) two oxygen sensors, and they compare values to see if your catalytic converter is functioning normally, and if the fuel/air mixture is correct (by checking to see what's in the exhaust gas).
One oxygen sensor is located in front of the catalytic converter (upstream), and one is located after the converter (downstream). Either one of these may be causing the problem.
Could be a loose connection, or the dang things are broke. Mine, thankfully, was the upstream oxygen sensor. $90 for part, and I changed it myself (it looks like a spark plug sticking out of your exhaust line) on the Civic. The downstream oxygen sensor is about $200.
The ECU code will tell you which, if any, parts are showing errors. Have a friendly mechanic hook up their computer and tell you. Shouldn't cost anything if you're nice to them.
P.S. - in my situation, the light came on, and after I reset the ECU it stayed on, so the computer said the BANK 1 SENSOR 1 had an error. The engine itself didn't show any rough idle or any other problems, and I drove it for another week or so (not racing or hard driving).
After I changed the oxygen sensor, I had to reset the ECU again, and the light has remained off since. No change in engine performance, but I may see a slight change in mileage...