I'm a vegetarian.  Do you know the history of vegetarianism? 
From what I know Vegetarianism got it's roots in ancient India and ancient Greece
What vegetables did the people eat during that time? 
Much the same as what we eat today. The concept is not to eat flesh. Some people include dairy and eggs while others don't.
So the practice is pretty much static? Has any advancements been made in it since the inception? 
Other than things like meatless meats it's stayed the same. It's all connected with the idea of nonviolence towards animals. It was originally promoted by philosophers and religions
What other areas of the world is it practiced in? 
It's practiced everywhere in the world to some degree. Vegetarianism was almost gone in Europe but reemerged during the renaissance and got more popular in 19th 20th centuries