The central theme of the movie seems to be in line with the book, namely, the judgements we make based on assumptions/presumptions are often quite false and reflect poorly on the person or community making the assumptions.
The story features two significant false assumptions that stem from a popular but unfounded bias. The lesson of the story is related to how these biases can keep us/people from recognizing (and even beginning to really look for) truth.
Gregory Peck has played a number of roles that deal with bias; his role as Atticus Finch befits his political leanings. The film, like the novel, exposes the prejudices and biases of people.
I would say that the meaning of the film is the same as the meaning of the book. Both made a statement about racial inequality, injustice, and innocence. The movie followed the book very closely. I think they did an excellent job of maintaining the themes and ideals found in the book.
The Academy Award-winning film adaptation of To Kill a Mockingbird was in response to the Pulitzer Prize-winning novel--it was terrific book that deserved a prompt and equally high quality film version, and that's exactly what transpired. It deals with racial inequality in the 1930s that was still a highly pertinent subject in the early 1960s; and it deals with children growing up in a changing world, another important theme that encompassed the decades of the 'Sixties and 'Seventies and beyond.
One explantaion says that To Kill a Mockingbird offers an example of how fear leads to prejudice and understanding leads to tolerance.