The theme of the mockingbird is first introduced in Chapter 10 when Atticus reminds Jem, who is practicing with his new air rifle, that
"I'd rather you shot at tin cans in the back yard, but I know you'll go after birds. Shoot all the blue jays you want, if you can hit 'em, but remember it's a sin to kill a mockingbird."
Miss Maudie confirms the natural sweetness of the mockingbird in a later conversation with Scout, explaining that they don't harm crops and only "sing their hearts out for us."
Most of the children in the novel serve as human mockingbirds, as do some adults, such as Boo and Tom. The author adds further symbolism in Jem's and Scout's names: They are Finches, a bird with similar characteristics to the mockingbird. They symbolize innocence in an often cruel world that does not always treat such people justly. Jem's and Scout's lost innocence is one of the major themes that connects them with the mockingbird, while Boo and Tom are charged with acts--and punished for them (in Tom's case, with death)--that they did not commit.
Scout comes to recognize the symbolism between the bird and the man when she tells Atticus in Chapter 30 that charging Boo in the death of Bob Ewell would
"... be sort of like shootin' a mockingbird, wouldn't it?"
compassion: sympathy for the suffering of others, often including a desire to help
When the mockingbird is referred to in to Kill A Mockingbird, I believe it is Atticus that says it's a sin to kill one because they are innocent creatures and all they do is sing to bring happiness. (I'd check on who says it)
The one main mockingbird is Tom Robinson because he is innocent in the crime. But because of racism and other predjudices, people look at Tom and name him instantly guilty.
Think about their thoughts on Tom near the end and Atticus' thoughts aswell...were they racist?