The mockingbird symbolizes the good and gentle people because these are often the people who are taken advantage of by others because of their perceived weakness.
In the story, a mockingbird becomes a symbol for anyone who does no harm and yet is a target anyway. There are two named mockingbirds: Boo Radley and Tom Robinson. Boo is targeted because he is a shut-in and people don’t understand that he is shy. Tom is targeted because of his race.
Early on, Atticus warns Jem and Scout never to shoot a mockingbird. When they ask Miss Maudie why, she explains.
Mockingbirds don't do one thing but make music for us to enjoy. They don't eat up people's gardens, don't nest in corncribs, they don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird." (ch 10)
Mockingbirds do not do damage like some other birds do. There is no reason to shoot at them. They are sweet and innocent birds, just as some people who are targeted because they are different are also innocent.
The first direct comparison of the person to the mockingbird is actually after Tom Robinson is shot. Mr. Underwood seems to echo Atticus’s words.
Mr. Underwood simply figured it was a sin to kill cripples, be they standing, sitting, or escaping. He likened Tom's death to the senseless slaughter of songbirds by hunters and children… (ch 25)
Underwood’s comments reinforce Tom’s role as a mockingbird. He was a sweet and innocent man, and he was targeted by Mayella because of his kindness, and targeted by the jury because of it too. He would not have ever been in the position to be accused if he hadn’t been kind enough to help Mayella out.
The second comparison comes when Scout realizes that Boo Radley has saved the children and does not want to be recognized for it. Atticus asks Scout if she can understand why they should not tell everyone what Boo did.
"Well, it'd be sort of like shootin' a mockingbird, wouldn't it?" (ch 30)
Scout acknowledges that Boo Radley is an innocent, and might end up the subject of too much public scrutiny and attention if anyone knew. The ladies would bring him food and people would want to talk to him.
In the end, one of the mockingbirds is shot and the other is left alone.