Tyres are grooved at the contact surface

Your shoes are answer for why?

And how? its moulded not cut.

They use a CNC machine to cut the mold. The grooves are the ridges and the protruding parts pockets.

Google for tyre molds images to see what they look like and also what a mold looks like.

Note that both words mold and mould are used.

Tires are grooved to let water escape from the contact surface. If it's raining.

They groove the tyres on F1 cars to slow them down.

More importantly, consider the shape of the surface round, and the shape of the same surface when forced to flatten (which is what happens when it is against the road).

If you have access to a flat tire (or just let the air out of one), you can push a flat piece of thick glass against it to flatten a small section, and you will see an amazing feat of design at work. This is a high science involving topology, trigonometry, and a great imagination along with a handle on several areas of science.

CJM