Can someone help me with the difference between non-reactive cookware and regular? I have read recipes that call for non-reactive, and I don't know how it will effect the food.
Non-reactive means, it doesn't tend to react chemically - with strong acids, salty foods as well as more esoteric reactions - with commonly cooked foods. Aluminum, bare iron, steel and copper are all fairly common "reactive" materials that cookware might be made with. In some cases, like copper, chemical reaction and physical abrasion can, at least potentially, toxic. In most cases, it "just" may introduce unpleasant flavors or colors - eggs in aluminum is a classic example, foods cooked for long periods in any bare metal will often pick up a slightly "metallic" edge (think bad canned soup) that's really unpleasant.
Non-reactive materials are just that - for practical purposes they don't chemically or physically intereact with foods. Glass and glassy-ceramics (like Corningware) are probably the most non-reactive, strictly speaking, but good quality stainless steel and enamel over metal are very non-reactive, too. Non-stick coatings would also count as "non-reactive" by and large.
As with any material for any purpose, there is single ideal. They all have advantages and disadvantages, so which is the (dreaded) "Best" depends entirely on its intended use. Even bare copper, for example, which you'd be crazy to use for general purpose use, makes the best beaten egg whites you'll ever see and allows for the "finest" control over heat practically possible for candymaking, where the potential for copper contamination is minimal because sugar itself is pretty non-reactive and you don't cook the stuff for very long, albeit over high heat. Bare steel and iron can be seasoned to minimize rusting and improve cooking qualities, and their relatively high thermal mass, strength and cheapness are all desireable under the some circumstances.