Why do tires have grooves?

Not all tyres have grooves. Take the "slick" tyre - it does not have grooves. It is used always in racing (as it is illegal to use on most countries roads) and only in dry weather (permitting).

"Normal" tyres have grooves, as a channel to expel water from the surface of the tyre. Without these "grooves", driving in the wet would be a hair-raising experience, as the tyre would aquaplane on the water giving the driver, no grip or control.

This is also the reason that most countries have a limit on the tread depth, to ensure that the channels are large enough to expel any water away from the surface of the tyre.