Personification is the act of attributing the qualities of a human to something that normally does not have those qualities. Inanimate objects are frequently personified as a means of revealing their relationship to humans.
There are abundant examples of personification in this story, because the house was designed to function more as a member of the family than as a simple machine, and so both its literal design and the way in which it is described make use of personification to illustrate this intended relationship. One example is the use of the term "bones" to describe the wooden frame that supports the house. They are mentioned to be made of oak, which might suggest that the house is still being made with traditional materials and appearances in mind (oak is a common choice for housing) and that the house is very much an amalgamation of natural materials, technology, and the personification of these elements that make it seem to be alive.
As the house burns at the end of the story, the fire is said to be causing it to shudder right down to its bones, which is probably a literal description of what is taking place, but by using the term "bones" it reinforces that the house is alive and its components are treated like the parts of a body.
The significance of this is that the house is lent more of a personality, and more empathy, than we might give to a simple burning home. The house is literally able to say that it's on fire, and at some point we have to establish that there are certain triggers we possess as humans that require us to make a choice as to whether something should be considered alive or worthy of an emotional reaction. By personifying the house we are, perhaps, intended to be made uncomfortable by its destruction in a way that we would not feel if the house were merely a computer and wood.