I'm glad that I'm not the only one puzzled by this. This is how it was explained to me:
The engine computer uses a bunch of controls to "guess" that it is time to change the oil. Then the overhead indicator notifies the driver. After the oil change you can reset your indicator and all is well.
Here's the weird part. If you decide to change your oil before the indicator come on (like if you change your oil every 5000), the computer can't detect this. Even if you try to reset the indicator before it trips, it won't reset. This is why sometimes the indicator comes on soon after a service. Kind of annoying, so I always keep track of my mileage AND hours at oil changes.