Vegetarians are people who do not eat meat products and may also not consume dairy products or eggs. They may do so for health reasons or for philosophical and moral reasons. Some people, such as Seventh Day Adventists, are vegetarians because of their religious beliefs.
Many people eat plant foods simply because they are cheaper than animal products.
Loving animals is all you really need to do to start being into animal rights. The animal rights movement is about putting an end to animal suffering. Animals suffer in many ways most people don't know about. They are used as test subjects for many products. This testing often is very painful.