When your English teacher talks about a thesis or a thesis statement, he or she is usually referring to a short, debatable claim around which you structure a paper. A thesis is a pithy statement of your main argument. It's what you're going to prove.
A thesis is usually called for in assignments that deal with academic argument, and we're going to give all you Shmoopers out there a big tip: if you're English paper doesn't have a thesis, well, that's a Big Problem. Get one, and fast.