The "tread" is the part of the tire that is supposed to touch the ground. A tire with no tread would be a tire that is not supposed to touch the ground.
You may be wondering why tires have a pattern of grooves (a.k.a., voids) in the tread. They're for bad weather. The grooves allow rain, and (if they're wider) mud and snow to squelch out from under the tire so that the tread can come into contact with something solid on which to get a grip.
When your tires have 2/32" tread depth left you need to replace them.
If you're having to put air in your tires frequently then your tires probably need replacing. Also if the tread on the tires is worn down they should be replaced (a symptom of worn tread is the tires squealing on the road for no apparent reason).
More than narrow tread tires.
Tires have molded indicators called "wear bars." If these are visible across the tread pattern, your tires need to be replaced.
I inspect the tire and measure the tread depth.
There are tread wear indicators that are in the tire itself. When the tires need to be repalced theese indicators show.
In the tread there are small 'bars' at the bottom surface about 2-3 mm high, when average tread wear is down to these 'bars' you should get new tires.
If you want traction you need the tread. Smooth tires are only used for racing.
A good test is to take a penny and place it in the tread grove with the head of Lincoln facing down. If you can see the top of Lincoln's head you need new tires. If the tread is worn more on the inside or outside you need a front end alignment. If the tread is worn on the outer edges you are running the tires with too low air pressure. Worn in the center, too much air pressure. Of course dry rotted and cracked tires need replacing no matter the tread depth.
Minimum tread depth for all 4 tires is 2/32"
You put a penny into the tread with Abraham Lincoln's head facing the tire. If the tread covers up Abe at all, then you're good. If not, get new tires!
Eventually, you will notice that your car is losing traction due to tread loss, especially on wet surfaces. You'll also notice that you may not be getting the mileage out of your car that you used to. A good, simple way to check the tread is with a quarter. On most tires, when the tread is lower than Washington's nose, it's time to take your car in and see of you need new tires.