Think about this question personally for a minute. What does it mean to you when you hear that a person is the same in his own house as he is in public? The answer to this question is as simple as it sounds. Basically, Miss Maudie is saying that Atticus does not have anything to hide. He's not putting on a pretense in front of his neighbors or his family. Atticus is exactly as good hearted, full of integrity, and willing to do the right thing no matter who is around. He is not trying to impress nor offend anyone.
Miss Maudie is a lifelong friend of Atticus'. Aside from his own brother and sister, in the town of Maycomb, she has known him the longest. This quote is a testament to Atticus' character from a very trustworthy source.
It means that Atticus Finch is not a hypocrite. It means that he respects everyone, whether they are his children, his relatives, his neighbors, his colleagues, the townspeople, etc. He is not two-faced, wearing one face while at home, and the other face while out in public. He is a man of his word, and his word is the same for his own family and for others.
Atticus proves this at the end of the story when he thinks Jem is guilty of stabbing Bob Ewell. He tells Heck Tate that he expects Heck to treat Jem just as any other person who committed a crime. He explains to Heck Tate that he believes his son should have no special treatment, just because he is the son of Atticus Finch.
Read more about Atticus Finch's character here at enotes at the link below.
He is not a hypocrite and he treats people the same and he treats those inside his house. He does not care if he is white, he will still take up an African American mans case because it is the right thing to do and is also where justice resides.