Tom Robinson was a black man who was tried for, and convicted of, raping a white woman, Mayella Ewell. He was clearly innocent, as was proven by the most important character in the trial -- Atticus Finch.
Atticus was Tom's lawyer. His commitment to justice and his intelligent questioning of witnesses had a huge impact on the trial because they proved (to anyone with a fair mind) that Robinson was innocent.
In his questioning of Mayella Ewell and her father Bob, Atticus proved that Tom Robinson could not have raped Mayella. He did this most clearly by demonstrating that Tom was not physically capable of holding Mayella and beating her in the way that the Ewells said he did.
Throughout the trial, Atticus showed his devotion to justice and to treating people fairly (these are two major themes in the book). Because of this, the trial is one of the most important parts of the book.