Mockingbirds represent harmlessness and a need for protection in the novel. A number of characters are related to these notions, with Tom Robinson and Boo Radley directly connected to mockingbirds in the text.
Atticus Finch and Miss Maudie help to articulate the meaning of mockingbirds as a symbol in the text.
As Miss Maudie Atkinson explains, it would be thoughtlessly cruel to kill innocent creatures that "don't do one thing but make music for us to enjoy."
Atticus Finch is another character that can be understood as a mockingbird, along with Scout, Jem and Dill. These characters strive to do good and require more protection than they realize. We see this with Atticus in particular as he repeatedly assures himself and his family that Bob Ewell will not try to harm them.
We can see the place that mockingbirds have in the text through the above examples and evidence. The other part of the title, "to kill", may be seen as referring to the injustice that is done to Tom Robinson, in particular, and to Boo Radley more subtly.
Both of these characters function as a "mockingbird", doing no harm and also needing more protection than they can give themselves. The legal injustice done to Tom Robinson proves to be fatal when Tom is killed trying to escape from prison. Even here, however, Robinson displays a kinship with the harmless mockingbird.
Even in his escape he shows courage – surely knowing that his escape attempt is unlikely to be successful, but thereby putting an end to the ongoing trauma to all involved.
When Atticus says it is a sin to kill a mockingbird, he is saying this because mockingbirds do not do anything to harm or annoy us. All they do is sing to us.
There are two main symbolic "mockingbirds" in the story. The first is Tom Robinson. This is because he really did nothing harmful to Mayella. The only thing he really did was help her whenever she needed it.
The second is Boo Radley. This because it would be a sin to harm him by giving him a spotlight he really doesn't want. He just wants to be left alone.