If you recall from chapter 10 Scout asks Miss Maudie about something Atticus says--"Shoot all the bluejays you want...but remember it's a sin to kill a mockingbird" (98). Scout needs clarification because she's never heard Atticus refer to anything as a sin before. Miss Maudie answers that mockingbirds "don't eat up gardens," "nest in corncribs" and that "they only sing their hearts out for us," which basically means they are harmless creatures who can only bring joy. Now if you apply what you have come to learn about Arthur Radley, you will find that he is as harmless as a mockingbird and his only true actions have been at the least nice (leaving presents for the children), and, at the most, lifesaving (his actions from Halloween night).
At the end when Atticus mistakenly believes Jem killed Ewell, Sheriff Tate affirms that it was not Jem but Arthur who killed Ewell and Tate continues by telling Atticus that as far as he is concerned Ewell killed himself and justice has won. When telling this to Atticus Tate specifically uses the word sin to describe exposing Arthur and the truth of the situation. After Tate leaves, Atticus asks Scout if she can understand but it's Atticus that needs the situation to be explained to him and she has to reaffirm to him that it would be "like killing a mockingbird" (290) reaffirming that it is a sin in the one way that she and Atticus understand: it's simply wrong to bring harm to a creature that only brings joy.
By extension you can see how Scout has grown up and is able to understand that sometimes justice isn't a black and white issue, but more of a grey one.
Harper Lee's novel To Kill a Mockingbird depicts a mocking bird as a bird that does nothing, it only sings. It is a living being, basically, that is incapable of hurting anyone because of its size, its lack of malice, and its inability to overtake someone even in self defense.
Similarly, Boo Radley represents a living human being whose nature is not what his accuser wants the jury to believe. He entered the Ewell home with the purpose of helping. He was harassed by the woman and then accused of raping her. This is a direct lie that would make Boo sound like an evil man, which he is not.
Putting Boo in jail, hurting him, or anything would be like jailing, hurting, or killing a mockingbird: Something that did not hurt anyone for any reason and whose size in society is so small that he cannot overtake the system even to defend himself. That is the symbolism behind the mockingbird.