Vegetarianism has been around since ancient India and Greece. I have several friends who are vegetarians and say they love it.
Are there health benefits to it? 
Some think abstaining from animals does lead to health benefits but most vegetarians do it out of respect for life.
What do they call people who do it based on mental issues? Like meat makes you queasy. 
I don't know if they have a name but there is a field of research in the psychology of eating meat.
When does it date back too? 
The ealiest records we have of vegetarianism dates to the ancient Greek civilizations in ~100 CE