So I've been "studying" java for two semesters, and my teacher is not what you would call the best. I was just wondering if any of you guys could help me out with some questions I have...
What is a recursive termination condition and what happens if a recursive function does not contain this condition?

A recursive termination condition is generally called a 'base case' I think. So go look up 'recursion base case' on google. I've never even heard it called a recursive termination condition before. And a base case is necessary because without one, your method will keep recursively calling itself, and will have no mechanism to stop. For more info - use google. :)

recursive termination condition is also called a stopping state...so im guessing your right?
without a stopping state, it would just keep calling itself right?

If a recursive function has no base case, it will not return and you will get a stack overflow.

recursive termination condition is also called a stopping state...so im guessing your right?
without a stopping state, it would just keep calling itself right?

Yes. The stopping state is called a 'base case', and there can be more than one. And yes, without a base case, it would keep calling itself, leading to a stack overflow as noodle says. In java it would just throw a StackOverflowException. But in any programming language, the concept is the same. Simple example (you'd never code anything like this, but just as an example):

public void myMethod(int current){
if (current <= 0) return;
current--;
myMethod(current);
}

Now consider what would happen if the base case (the first line of code in the method) was taken away. It would never stop calling itself.