The thing that determines whether ozone is good or bad is its location.
Ozone is "good" when it is in the stratosphere. The stratosphere is a layer of the atmosphere starting at the level of about 6 miles (about 10 kilometers) above sea level. The stratosphere naturally contains about six parts per million of ozone, and this ozone is very beneficial because it absorbs UV radiation and prevents it from reaching us (see How Sunburns and Sun Tans Work for a description of the damage that UV radiation can cause to skin). Check out this page for a good description of the chemical reaction that allows ozone to absorb UV light.
Ozone is "bad" when it is at ground level. Ozone is a very reactive gas that is hard on lung tissue. It also damages plants and buildings. Any ozone at ground level is a problem. Unfortunately, chemicals in car exhaust and chemicals produced by some industries react with light to produce lots of ozone at ground level. In cities, the ozone level can rise to a point where it becomes hazardous to our health. That's when you hear about an ozone warning on the news.
Here are some interesting links: