During the trial, we learn that Tom's left arm is withered due to a childhood accident. This means that he simply could not have committed the crimes for which he's been charged. It would've been physically impossible for him to have attacked and raped Mayella.
In a fair trial, this information would've blown the prosecution's case right out of the water, but this is the Deep South in the 1930s; this is a place and a time in which racial prejudice is deeply ingrained in every aspect of life, including the criminal justice system. To the members of the jury, and to most white folk in town, Tom is guilty simply by virtue of being a black man charged with attacking a white woman. This is a legalized lynching, nothing more, and the jury understands what's expected of them. In spite of overwhelming evidence to the contrary, they convict Tom Robinson.