A vegetarian does not eat cows, chickens, fish, and other animals, including anything made with meat, gelatin, rennet (in cheese), and vitamin D3 (added to dairy).
To avoid killing animals, some people avoid dairy and eggs. Dairy cows and egg-laying hens are killed when they no longer produce milk or eggs. Their male offspring: calves are made into veal, and chicks are thrown in the trash.
To avoid killing animals, some people avoid clothing with animal skin and hair. Buying leather further increases killing, because it decreases meat prices, increasing meat consumption.
There are many other reasons to avoid dairy, eggs, and other products from animals. They contribute to human health problems. Their production is very bad for the environment. And, farm animals suffer immensely. Some people avoid those products for religious reasons. Plus, eating only foods from plants causes fewer plants, trees, and natural habitats to be destroyed.
Some people expand their circle of compassion beyond animals with a spine to include bees, and therefore don't eat honey.
Vegan means having none of the animal-derived products mentioned above.