If you Give Me A Break you are giving me an opportunity or letting me off, usually after I've done something wrong or been perceived to do so. This phrase comes from the early street performers who'd break halfway through their act to pass a hat around and collect money for their performance. The phrase was picked up during the 19th century by the criminal and vagrant community who had pass a hat around for a friend on their release from prison in order that they had not have to return to the world totally penniless. That person was considered to have been "given a break."