What three houses are important to the narrative of To Kill a Mockingbird and why are they important?

The three houses that play key roles in To Kill a Mockingbird are the Finch home, the Radley home, and Miss Maudie's home.

• The Finch home

The significance of the Finch house is obvious since much of what occurs inside or outside of it generates the narrative of Harper Lee's novel. The house is where the children feel safe and loved; even Dill Harris seeks it as a refuge from his emotional neglect. At the Finch home, Calpurnia is treated as a part of the family. In the evenings, Atticus sits behind the Mobile Register and reflects upon many things in the safety of his own house. This is his method of hiding his inner conflicts.
In Chapter five, Miss Maudie tells Jem and Scout about how genuine Atticus is when she says,

"Atticus is the same in his house as he is in the public streets."

When the men from town come to talk to Atticus, they stand in the front yard and do not enter the house, thus displaying their respect for the Finch family and their privacy. That evening, Atticus leaves his house and sits in front of the jailhouse door, risking bodily harm when he could be within the safe confines of his home.

It is in the yard of the Finch house that the children play and try to spy on their neighbor, Boo Radley. It is on the porch of the house that Jem tells Scout he does not want Atticus to catch his lie about losing his pants, so he runs back to the Radley house and retrieves them. And, it is in the Finch house where Boo is afforded safety and given much gratitude from Atticus when he tells Boo, "...thank you for my children."

• The Radley house

In contrast to the Finch home, the Radley house is described by Miss Maudie as "a sad house." She says there is no way to know what abuse has gone on inside the Radley home. Aware of how Mr. Radley, who was a "foot-washing Baptist," used the Bible against Boo, Miss Maudie intimates that there were tragic episodes inside this house. Unlike the Finch children, who can ask their father anything, Boo has been silenced and made a prisoner in the house for many years because of his youthful indiscretions.

For Dill, Jem, and Scout, the Radley house is one of mystery and curiosity. They attempt to communicate with Boo, but Nathan Radley, who assumes the role of his father after the man's death, fires his shotgun as a warning to the children. Nevertheless, Boo attempts to establish a relationship with Jem and Scout by leaving things in a knothole of a tree that the children pass on their way home from school. Nathan stops this communication, too, by putting cement over the knothole. 
Fortunately, Boo continues to listen for and watch Jem and Scout, perhaps living vicariously through them. On the night of Bob Ewell's vicious attack upon the Finch children, Boo braves leaving his house and with courage he saves the lives of the children. For the first time, the two occupants of the Finch and Radley houses become more neighborly when Boo enters the Finch house, later walking home arm-in-arm with Scout. Afterward, as Scout stands on the Radley porch, she perceives things differently and more maturely. Truly, the Radley house has played an important role in the lives sheltered by the Finch house.

• Miss Maudie's house

Across the street from the Finch house, Miss Maudie's house and yard always welcome the children. Hers is much like a grandmother's place; the Finch children are allowed to play and have certain privileges, such as playing in one yard as long as they do not disturb the grapevines. Miss Maudie will explain almost anything asked by the Finch children, while at the same time teaching them kindness and thoughtfulness. She invites the children into her house for tasty desserts that help heal whatever is bothering them. Miss Maudie's house is often a refuge for Jem and Scout.

Much like the Finch house, Miss Maudie's house is positioned as a comfort and defense from the pettiness and gossip on the outside. Miss Maudie dismisses the gossip about Arthur Radley as nonsense. Like a good neighbor and friend, Miss Maudie also defends Atticus's decision to take on Tom Robinson's case.