For what reason does the mob want Atticus to turn over Tom Robinson?

An angry, drunken mob has descended upon the jailhouse, where Tom Robinson is being held prior to his trial for the rape and assault of Mayella Ewell. This is precisely what Heck Tate had feared would happen when he talked to Atticus earlier. At that time in the South, lynchings against African American males were depressingly common. Such extra-judicial murders had nothing to do with justice; they were simply a way of reinforcing the existing system of racial oppression. Men could end up being lynched on the flimsiest of pretexts. If an African American male so much as looked at a white woman the wrong way or spoke out of turn, he could soon find himself brutally murdered.
Most of the townsfolk of Maycomb have already concluded that Tom Robinson is guilty before they've even heard the evidence against him. He's a black man who's been accused of attacking a white woman; as far as they're concerned, that's all the evidence they need. But some of the men from the backwoods are not even prepared to wait for the trial; they want to carry out their own kind of "justice" by dragging Tom Robinson from the jailhouse and lynching him.