Tom Robinson was once in a fight with another man, and served thirty days for disorderly conduct. As Tom describes, the other man cut Tom in the shoulder. Both men were convicted of the crime, however, the other man was able to pay the fine and did not have to serve any time. Tom could not pay and served thirty days in jail.
The significance of this information being brought up by Atticus at the start of Tom's testimony reinforces the idea that Tom has nothing to hide, that he has done nothing wrong.
Not only has Tom Robinson not been in trouble with the law before, but it appears the town knows he is not guilty at this time. However, being a black man accused of raping a white woman was enough to make him in trouble because he could not fairly defend himself.