This is an adjective that refers to cookware which has a special coating which has the effect of making food slide off or out without sticking. These days you can buy non-stick pots, pans, utensils, woks, and so on. They used to all be coated with Teflon, another product from DuPont, but there are other non-stick surfaces now.
Whether non-stick cookware is for you or not depends on your habits. It requires more care than regular cookware; you shouldn't heat it to very high temperatures on the stove or in the oven; you shouldn't use metal utensils on it or you'll scratch the coating and it will eventually peel away; you shouldn't scrub it with an abrasive scrubber. Thoughtless roommates can destroy a nice pot forever in 2 minutes. However, if you can manage with these restrictions and control who uses your stuff, then non-stick cookware can be awfully convenient. A simple soak and wipe with soapy water is all that's needed to remove any food that might temporarily have been lodged on.
If you're not sure, buy one and see. I recommend starting with a frying pan or wok, and not the bottom of the line either. Ideally, the metal cladding should be fairly heavy, otherwise it will just buckle quickly. So buy a medium-priced one and try it out for a while and see how you like it.
The aspiring gourmet should note that non-stick pans can never brown food as well, and thus will not yield the perfect fond that is the part of the reason why restaurant sauces are so much better than homemade ones. My sauces are never that good either, but sometimes close; I have both regular and non-stick frying pans in my house. I swear, however, by my non-stick wok, for reasons I have detailed elsewhere.