The wall is a wall-to-wall circuit TV they have installed in their parlor. Mildred is obsessed with it. She had the TV installed on three walls, but she wants a fourth wall installed also. Mildred is interacting with the people on the walls.
"It's really fun. It'll even be more fun when we can afford to have the fourth wall installed." (pg 20)
The family are the characters in the walls that interact with Mildred. They are the uncles, aunts, cousins, nieces, and nephews that lived in those walls. Basically, they are TV characters. Montag had
"....taken to calling them relatives from the very first. " (pg 45)
The walls are one controlling factor of the people. People no longer read, so they watch television, and they are given a script on how to interact with it. They are told what to think and say, and the characters become real in their lives.
In Fahrenheit 451, the parlor walls are a form of entertainment that most people have inside their homes. Specifically, they are television screens which cover the surface of an entire wall, and we know from Part One of Fahrenheit 451 that Mildred and Montag have three parlor walls installed in their living room. Once the walls are turned on, they "bombard" the viewer with loud music and bright colors. The walls also play shows featuring the "family." These shows, often based on plays or comedies, feature recurrent and recognizable characters, like the White Clown, and are interactive. Mildred, for example, loves to take part in shows with the family and, in Part One, is learning a script for a forthcoming play.
For people like Mildred, the walls and the family have become part of everyday life. She is absorbed in this form of entertainment to the point that she is completely ignorant of the world around her and its problems.