In Harper Lee's To Kill a Mockingbird, Scout realizes several things during Tom Robinson's trial.

First of all, she realizes that Atticus was appointed to be Tom's lawyer, and he had to do it whether he wanted to or not, though I don't think it would have occurred to him not to. He observes later that every lawyer has a case that has a profound effect on him, and he expected this was the one for him.

When Atticus has Heck Tate testify to Mayella Ewell's injuries, we find that they are all on the right side of her face. This would mean that she was struck by someone left-handed. Scout understand this, and understands the implications of this information when Atticus exposes to the jury at Bob Ewell is left-handed, but Scout doesn't think this means anything because Tom Robinson could also be left-handed.

Scout soon realizes that Tom could not have done the damage to Miss Mayella as she and her father claimed. Tom's left arm had been caught in a cotton gin, and he could not use it: it was difficult to keep in on the Bible when he was sworn in.

Scout also comes to a realization about Mayella.

'Would Miss Mayella talk to you?'

'Yes, sir, she talked to me.'

As Tom Robinson gave his testimony, it came to me that Mayella Ewell must have been the loneliest person in the world. She was even lonelier than Boo Radley, who had not been out of the house in twenty-five years. When Atticus asked if she had any friends, she seemed not to know what he meant, then she thought he was making fun of her. She was as sad, I thought, as what Jem called a mixed child: white people wouldn't have anything to do with her because she lived among pigs; Negroes wouldn't have anything to do with her because she was white...Tom Robinson was probably the only person who was ever decent to her, and when she stood up she looked at him as if he were dirt beneath her feet.

So Scout realizes several things during the trial. She realizes that Tom could not have attacked Mayella because when he gets up to be sworn in, his arm is totally useless, falling limply at his side so he cannot keep it on the Bible's cover.

After Tom begins to provide his testimony, Scout also realizes what a sad and lonely person Mayella is.

Finally, and ironically, Scout notes that Tom has probably been nicer to Mayella than anyone else and yet she treated him like a criminal: and he is not.

Scout actually comes to a few important realizations.  By the trial, Scout has grown up considerably and is starting to think more like an adult than a child.  She realizes that Tom is innocent, and Jem indeed does not think he'll be convicted.  She notices that Tom is crippled, and he could not physically have committed the crime.

Another realization that Scout comes to during Tom's trial is that Mayella is a simple girl who leads a hard life and does not many friends.  Scout actually begins to feel sorry for Mayella, even though she has done a terrible thing in going along with accusing Tom Robinson.  This is a big step for Mayella because she is beginning to take Atticus's advice and walk around in another person's skin.