Most vegetarians prefer not to have their food or utensils touching meat or other animal-derived foods. This preference is similar in concept to keeping kosher. In practical terms, some individuals who have "kept vegetarian" for years may endure significant intestinal distress if they ingest meat or grease. When you're cooking for your vegetarian guest, please keep utensils separate (for instance, do not use the same spoon for deglazing the roasting pan and then serving plain steamed vegetables) and do not label a food "vegetarian" if it includes chicken, beef, or veal broth.
This article about hosting a vegetarian guest for Thanksgiving includes recipes and delves into some etiquette and lifestyle concerns that I've not seen discussed before.