When you are writing a thesis statement this is a statement in the introduction of your paper in which you take a stance on a topic and explain what you will support (in an argumentative paper) or what you expect to find (in a research paper).
If you are writing a paper about dogs versus cats you first want to discover what stance you want to take. An example of this would be "Cats make a better pet for a professional who is not home a lot because they require less hands on care on a daily basis." This shows what you are going to explore within your essay and what topics the reader can expect to see within the paper. First you will explore what kind of care a cat needs, then you will explore how a single professional who is not home a lot would benefit from having a cat instead of a dog who may need more hands on care.