Tires are the only part of your vehicle that makes contact with the road. A good driver on bad tires is still going to have a bad time driving on them. If your tires look like they’d be suited for the drag strip, you need to replace them. If your tires have a bunch of really cool metal wires poking out of them where tread used to be, you REALLY need to replace them. The same applies to checking your tire pressures. If they are inflated too high or too low your car's grip is going to be compromised.
Drive on, friends!