Pans that are thought of as reactive are aluminum, copper and cast iron. When used with certain foods containing acids, like tomatoes, the pans can impart a metallic flavor to the food as well as discolor the food during cooking.
By contrast, nonreactive pans are ones thought to be safe with all foods, which refers to pots and pans made out of stainless steel, enameled cast iron, glass or clay. Stainless steel is the most common nonreactive material used for stovetop pans. Many pans also come equipped with a nonstick coating, which is also nonreactive.
If you have aluminum or copper pans, you can certainly still cook with them, just not with certain foods. Acidic ingredients like tomatoes, lemon juice and vinegar can react with the pans, causing the metal to leech flavor into your dish. But these pans are still good for searing meats, sauteing vegetables or boiling water for pasta or eggs.
When comparing reactive and nonreactive pans, the secret is all in the materials. Use copper or aluminum pans for cooking meat evenly, but pick up a stainless steel pot for whipping up a batch of tomato sauce.