What's this button next to my gear stick driver side in my ford focus 2001?

I have never noticed it but there's a button next to my gear stick look like a fan caughing here is a image
https://drive.google.com/...p=drivesdk

Traction control button. There may be times that your car has so little traction that it will not allow your car to go. You could heed that advice, or you could push the button and use what little traction you can find.

I think that is the calibrate/check button for your tyre pressure detection.
If it is the same as mine a short press will confirm operation, a long press will initiate a system calibration.
The system works using your ABS sensors. As a tyre deflates it's rolling diameter reduces meaning that its average rate of rotation increases vs the other wheel on the axel. That triggers a warning.
To calibrate: while driving, press and hold the button till you heat a "ping" sound, release the button and keep driving for at least a couple of hundred yards. You should do this after fitting new tyres or after inflating existing tyres

Boy oh boy. You gave your best answer vote to someone who was not even close to providing the correct answer.

Did you refer to your owner's manual? I suggest you do and refer to page 144 for information regarding your Ford's automatic transaxle operation.

It might be the snow/ice button that prevents wheelspin by making the gears start in 2nd Instead of first