That sounds very like an AW 70/71/72 gearbox with switchable overdrive. To be honest, it's more a case switching out the overdrive as if you put it in "D" and press the button on the side, you should get an orange arrow light up in the sintrument cluster. This signifies that overdrive/4th gear isn't operative.
If you drive off like that, you'll find it changes from 1st to 2nd to 3rd and no matter what speed you do, it won't go into 4th (overdrive) until you press that button again to release the inhibitor on overdrive/4th.
It's handy for overtaking when you don't want full kick-down but need a bit more than 4th gives you on part-throttle. In normal operation, find a car you want to overtake (while driving in 4th) and squeeze the accelerator gently then press the button in - it should immediately down-change to 3rd, orange arrow will appear and makes overtaking easier then once past, press the button again to return to 4th/overdrive.
Also if you are driving in mountainous areas or perhaps towing a heavy trailer, it's useful to inhibit 4th/overdrive to minimise the risk of overheating the transmission.
Note that if you've been driving with overdrive inhibited (orange arrow showing), when you move the lever from "D" it will automatically reset to normal operation, or at least should. Mine sometimes comes on randomly for no reason on start up, press the button and the orange light goes out, just a sticky relay i think.
Have a play with it along the lines of the above and see if it will benefit you when you're driving, if not then ignore it after but remember it's there just in case it throws a wobbler like mine sometimes does.
The only way that would have been a daft question is if you hadn't asked it to find out.
