There are several times where Lee uses the image of the mockingbird in her novel. All of them are significant as they speak of the central meaning of the book.
Mockingbirds are the creatures in the book that only help people. To use the words of Miss Maudie, they only do one thing - sing. They hurt no one and only make music for people to enjoy. This is why it is a sin to kill a mockingbird.
As to why Scout and Jem hear a mockingbird, there is a bit of foreshadowing going on. Like the other figurative mockingbirds that were hurt, notably Tom Robinson, soon Jem and Scout would be hurt as well by Bob Ewell in a vicious attack. In this sense, Scout and Jem are mockingbirds as well. Luckily for them, another mockingbird comes to the rescue and saves them - Boo Radley.
As was mentioned in the previous post, mockingbirds symbolize innocent beings throughout the novel. In Chapter 28, Jem and Scout walk by themselves to the Maycomb Halloween festival. As they pass the Radley Place, they hear the sound of a mockingbird, which is interrupted by the cry of a bluejay. This is a significant motif that Harper Lee incorporates into the children's "longest journey." Jem and Scout could both be considered symbolic mockingbirds, given that they are innocent children, who cause no harm to anybody. Interestingly, Jem and Scout's last name is Finch, which is a small, vulnerable song bird that is similar to a mockingbird. Bob Ewell would be considered a bluejay because he harms other people, similar to how bluejays disturb people's gardens. The fact that the mockingbird's song is interrupted by the squawk of a bluejay foreshadows Bob Ewell's attack on the children.