Non-reactive pans are pans whose material won’t react with certain ingredients.
Specifically, the concern is with certain acidic foods such as tomatoes, citrus, wine, chutneys, pickles, and cranberries. An interaction between them and the cooking dish they are in can either darken the ingredient or cause the ingredient to take on a metallic taste.
Metals that can allow this to occur are termed “reactive” — metals such as aluminum, cast iron and copper.
Copper pots are often lined with a thin layer of tin to prevent the reaction, but from time to time, they have to be surfaced as scratches, nicks and dings can expose the copper underneath. Enamelware can become reactive, if the enamel is chipped, exposing the metal beneath. Anodized aluminum is fine. Tin foil is one of the most reactive materials in the kitchen: don’t leave reactive foods covered with this for long.
Non-reactive material is glass, plastic, stainless steel, glazed ceramic, unglazed clay, CorningWare, or non-stick (which has the metal coated.) Calphalon and Alpholon cookware have non-reactive surfaces on them. Le Creuset has a porcelain surface over the cast iron.
Some say, though, that they’ve spent a lifetime cooking up tomato sauces in “reactive” pans, and have never noticed any difference, tastewise or otherwise, and that the whole worry is over exaggerated (aside from what can happen to tinfoil and tomato over a period of several days in the refrigerator.)