What about the trial is Atticus worried about?

Atticus Finch is a white lawyer representing Tom Robinson, an African American man on trial for raping and beating a white young woman, Mayella Ewell. Mayella's father, Bob Ewell, is the accuser; he is a horrible father and the real person responsible for violence against Mayella, but he accuses Tom.
Atticus is concerned because Tom has little chance of receiving a fair trial due to systemic racism within the town of Maycomb and its court system, and he is worried for Tom's physical safety because of threats made by many of Maycomb's townspeople. In a heated moment outside the Maycomb jail the night before Tom's trial, Atticus also becomes concerned about how his role in the trial could threaten his own children's safety.
As an African American man living in the fictional, small, southern town of Maycomb, Alabama in the 1930s, Tom's word against the word of the Ewells' will likely not be believed due to his race, even though Tom has committed no crime. Atticus knows this, and he also understands that the town's sheriff, Heck Tate, will testify against Tom, further strengthening the Ewells' case. Atticus is a man who passionately believes in justice and integrity, and it sickens him to know that the truth matters less than Bob Ewell's desire for notoriety.
Threats of violence against Tom and Atticus are made in chapter 15 as well, further concerning Atticus. At the beginning of the chapter, Atticus's children, Scout and Jem, overhear a heated conversation between Atticus and a group of Maycomb men who pay him an intimidating visit. Atticus tells the men that the truth will come out, the men become more threatening, and Jem interrupts their conversation when he worries for Atticus' safety. They approach Atticus again the very next day after church services with a similar message for Atticus about his reputation should he continue to represent Tom at trial.
Later in the same chapter, Atticus travels to the Maycomb jail to protect Tom from violence, since he knows that Heck Tate, the sheriff testifying against Tom, will likely do little to protect the African American man. Scout, Jem, and their friend Dill sneak off to the jail and narrowly escape violence themselves as they help to diffuse a crowd from a neighboring town who arrive hoping to lynch Tom. Here the reader sees Atticus's fear for his children's safety, who, up until this scene, have not been in any danger related to the trial.
Atticus is keenly aware of how little the legal system does to protect the rights of African American citizens and he knows there is little hope for justice for Tom. He also understands the threat of danger to his own children due to his decision to represent Tom Robinson.