Vegan
Vegan recipes have no meat, dairy, or eggs in them to accommodate for people who do not consume animal products. Just like everything in modern times, one word cannot cover the variety of ways people express their veganism. For general purposes, vegans exclude all food and products that contribute to animal exploitation, including food, cosmetics, clothing, and anything else.
Other Types of Vegans
Then there are more specific sects of vegans. Dietary vegans only eat plant-based for their diets, but don't worry about avoiding animal products in clothing and cosmetics. Within these categories, there are different levels of strictness of adherence. Non-vegan ingredients often show up in processed foods and no one realizes. Some of these ingredients include albumin, casein, carmine, gelatin, pepsin, shellac, isinglass, and whey.
Whole food vegans only (or as much as possible) eat vegetables, fruits, whole grains, seeds, nuts, and beans. They do not eat processed foods.
Raw food vegans go a step further and only eat raw foods, or foods gently cooked at less than 118 degrees F.
And the most extreme are also referred to as fruitarians, and they limit high-fat foods like coconuts and avocado, and only basically eat fruit, and sometimes other plants in small amounts.
Reasons to be Vegan
The reasons to eat vegan are as varied as the types of vegans. Most eat vegan for health reasons. There's more research every day that shows a vegan or mostly vegan diet has insanely good health benefits. Even eating vegan some of the time can provide health boosts.
Another large reasons people are vegan is to stop animal cruelty and exploitation. I would not recommend researching this any further unless you want to see some truly disturbing images and descriptions. Anti-animal cruelty vegans are often part of the reason people make fun of veganism like they do, unfortunately.