Worn tires affect your ability to control a vehicle.
Tires are about the most important thing on your vehicle. They are essential in everything we do when we drive, yet most of us don’t know how to tell if they’re too worn to be safe. One problem is that, when driving on dry pavement, worn-out tires don’t have a drastic effect on the vehicle's handling and will go mostly unnoticed. But with a sudden downpour, that same tire is unable to channel water away and will likely result in hydroplaning. Hydroplaning, which is incredibly dangerous, is when your tires can not displace the water on the road surface fast enough to stay in contact with the road surface.
This means your tire is riding on top of a thin layer of water and you no longer have control over your vehicle.
If you have any concern that your tires are getting too worn, stop into a tire shop and have them measure it with their gauge. Or, try out the coin test by following the instructions in the graphic.
Finally, and worth noting, driving safely can actually keep your tires from wearing prematurely (in addition to rotating them at least every other oil change). On my last two vehicles I squeezed over 80,000 miles out of a single set of tires. While tires are a lot better made today than even 15 years ago, the key is to avoid hard stops, aggressive turning, and sudden acceleration.