A thesis statement is the focusing idea, claim or opinion for your expository, analytical or persuasive essay. You create one that's specific enough to allow for limited research and discussion; it should also contain sub-topics -- middle and high schools call these "prongs" -- that you as the essayist will examine in separate sections. The thesis is the last sentence of your first paragraph -- the essay's road map, main topic and source of argument.
Everything's an Argument
Your argumentative thesis statement must present a claim -- an opinion, an interpretation, a cause-effect statement -- that you will prove with evidence; that burden of proof is why it is arguable. "The Holocaust was a horrible event" is not arguable; however, "the Holocaust could have been prevented had the United States entered the war earlier" would be. It would need solid cause-effect evidence before a reader would be able to accept it, and the argumentative essay that follows must present a case, logically and historically, that would support the idea of a preventable Holocaust.
Breaking Down Problems
An analytical essay breaks down an idea into its basic elements and then presents these elements, and your evaluation of them, to the reader. "Obamacare is a bad idea" is not analytical; "an analysis of the Affordable Care Act, known as Obamacare, reveals several possible difficulties in implementation" would be. This thesis is not an argument against the ACA; it examines problems the law might present in the future. Notice that, like the argumentative thesis, it allows you to branch into multiple areas of research, since there are "several possible difficulties" to discuss.
Expository is Explaining
An expository essay is the furthest you can get from an argument and still use a thesis; here it is not arguable or analytical, but a focusing tool for the information you will present. "Teaching is impossible these days" is argumentative; "teachers face multiple problems" is analytical. "A teacher's day contains many challenges, restrictions and rewards" would be expository; it doesn't weight the argument toward the negative, but intends to present, non-judgmentally, the parts of a teacher's single-day experience, good and bad.
Features of a Good Thesis
No matter what kind of essay you write, your thesis statement is the essay's central topic: examine your essay as you write to be sure it stays on track. The thesis is the essay's road map: be sure you follow each subject prong, like a branch in the main road, and return to the "road" each time. It's also an argument source: the whole of your opinion, and reasons for it, must be contained in your thesis. If your thesis is not centralized, multi-subject and argumentative, you need to rewrite.