The simplest definition of vegetarianism is a diet free of meat, fish, and fowl flesh. But eating habits of vegetarians cover a wide spectrum. At one end are lacto-ovo vegetarians, who avoid animal flesh but eat eggs and milk products. At the other end are vegans, who forgo eating (and often wearing) all animal-based products, including honey.
People who adopt a lacto-vegetarian diet abstain from all meat products, including eggs, but continue to eat dairy products. The advantage to this form of vegetarianism is you're less likely to develop a calcium deficiency due to the inclusion of calcium rich milk products.
A meatless diet can be healthy, but vegetarians -- especially vegans -- need to make sure they're getting enough vitamin B12, calcium, iron, and zinc. The Academy of Nutrition and Dietetics warns of the risk of vitamin B12 deficiencies in vegetarians and vegans.