Refurbished for any item usually means, "restored to like-new condition." A refurbished item usually has a warranty, whereas a used item might not. Often the warranty period is 30 days or 90 days (or some other term shorter than the original, new warranty), but sometimes it will have the same warranty as a new item.
Electronics can potentially have problems that were not caught during the refurbishing process, but if that's the case, it will probably be obvious either right away or after using the device for a little while. As kobaltz mentioned, you don't have to worry any more about bad pixels on a refurbished monitor vs. a new monitor, but if you do get one with bad pixels, you should be able to return it for a refund or exchange. On the other hand, if you were to buy an used monitor, you probably would be buying it as-is, without any warranty (unless the original warranty hasn't expired and you can get the manufacturer to honor it).
I've personally purchased a lot of refurbished electronics; ranging from a Sony Clie PDA, to PCs and laptops, to several motherboards, and they've always looked and worked just like new.