Question

How do the grooves of a tire increase the friction please explain using a diagram and a proper explanation

Answer 1

Grooves in tyres decrease friction. There is more to the story.

The purpose of Grooves is to effectively increase the friction.
As the other answer has pointed out, Grooves do decrease friction when you just look at the change in Surface area. (This is why you’ll see that F1 cars have no grooves)

But there is more,
The purpose of grooves is to remove water from the tracks during wet seasons.
This happens via capillary action.
This removes the thin layer of fluid which would have formed otherwise and effectively improving traction.