There are two pieces of evidence that discredit Bob Ewell completely and they have to work together. First, Atticus shows that Bob Ewell is left-handed, and Bob tries to show that he can use both hands, but it's too late. Then, when he asks Tom to rise after Mayella pointed him out, the courtroom sees the other necessary piece of evidence: Tom's left arm is 12 inches shorter than his right.
This proves it would have been impossible to leave the injuries on Mayella that were there. It also leaves the question on the table, if not Tom who? The fact that Bob was left-handed proved that it was possible he beat his daughter because the person who hurt her led exclusively with his left.
There are two main things that Atticus brings out that I think are important.
First, he brings out the fact that Bob Ewell is left handed. He shows that Mayella was almost certainly beaten by someone who was using his left hand.
Second, he brings out that Ewell does not call for a doctor. He says that this shows that Ewell knew Mayella had not been hurt by Tom Robinson. If she had, he would surely have called a doctor.