The title itself leads to a lot of symbolism. The mockingbird is intended to represent innocence and "killing" the mockingbird is the loss of innocence. Everyone experiences moments that permanently alter their view of the world. Some people experience these things as young adults and, unfortunately, some as kids who are forced to grow up too fast. A number of characters in the book are symbolic of the mockingbird, or the loss of innocence. Certainly Jem. Also consider Dill, Boo Radley, and Tom Robinson. They all experience things that take away some of their innocence through some sort of evil or wrongdoing.
After Tom is shot and killed, Mr. Underwood calls it "the senseless slaughter of songbirds."
Scout says that hurting Boo Radley would be like "shooting a mockingbird." (killing innocence)
Ms. Maude tells Scout "Mockingbirds don't do one thing but sing their hearts out for us. That's why it's a sin to kill a mockingbird."
Jem and Scout's last name is Finch, which is a type of small bird (similar to a mockingbird).
This question has been answered many times here on eNotes. Here is a comprehensive link for you: http://www.enotes.com/to-kill-a-mockingbird/search?q=symbols