Back in the 1960's, Uniroyal Tires advertised their "Tiger Paws" automobile tires by claiming that the treads of their tires gripped the road. Today, most people think that the tread of their tires also grip the road and that traction on dry roads comes from good, deep treads. The truth is that treads on your automobile tires has nothing to do with gripping the road. And in fact your tires increase their road traction as the treads wear down.
Your tires are the only contact you car has with the road. And that tire contact is only about the size of a man's palm at each corner. Needless to say that is not very much physical contact between the ground and the car. Your tires are doing a heck of a lot of work to put power down to the ground, or provide the stopping power to haul your car down from speed, or keep your car from sliding sideways off the road in a turn.
Cutting grooves (tread) in the surface of the tires reduces the contact patch with the ground and in turn reduces traction. When your tires are new and the treads are the deepest, the tread will "squirm" as you make a turn and slide just a tiny bit; most drivers will not notice this squirm. In racing series that require the sue of street tires with treads, racers will have the tread "shaved" down to reduce the tread depth and in turn reduce tire squirm. Formula 1 require treads to be placed into their racing tires to reduce traction and hopefully reduce car speed which can approach 200 mph even on typically tight and twisty F1 tracks.
If treads reduce tire contact with the road and consequently reduce traction, what purpose do treads serve? Treads are on your street tire to fight hydroplaning. That is the fancy name to describe how a smooth tire with little or no treads will ride up on a thin barrier of rainwater that builds up as you drive down a rainy road. Hydroplaning is a very dangerous condition because your tires have lost their contact with the road entirely. Treads allow your car's tires to pump water away from under the tires and help to maintain contact with the road. Tires rated for "Mud and Snow" have even broader treads to help remove those hazards from under tires and improve grip, but at the expense of less traction as regular rain tires on dry surfaces.
Many forms of auto racing will cancel their races on a rainy day, but some places in the world have too much rain to worry about a little precipitation and they press on in any conditions. In those cases, racing tires with chevron shaped treads are used. Looking like an endless line of wide letter V's, these tires are the most effective for pumping water away from the bottom of the tires. Water is thrown 20-30 feet into the air when racing cars are running at top speed on a wet track.
Throwing water high into the air is the least of your concerns in passenger cars driven on the street. But what you do want to be concerned with is that you buy the right tire for the conditions in which you are most likely to drive in. As much as an enthusiast may want to have the tires with little or no tread for the greatest potential traction on a dry surface, for practical purposes all street tires need to have treads to insure some wet road traction.