The phrase means that a house has the ability to communicate a narrative. This could be through its architecture. A Victorian - style house might tell a story of the era when it was built, with its elaborate details and design elements that were popular at that time. Also, the objects found inside the house, like old family photos or heirlooms, can contribute to the story the house is 'telling'.
Simply put, it means that the house is like a storyteller. Every mark on its walls, every broken window, or every added extension is a part of its story. It might tell the story of different generations who have lived there. Maybe the attic was once a hiding place for a child during a storm, and that's part of the story the house holds. The house is a silent witness to all that has happened within its walls and can reveal those tales.
It could mean that the house has a history or has witnessed various events and people over time, so it can convey that story to those who are observant or interested. For example, an old house with peeling wallpaper might tell the story of a family that once lived there but couldn't afford proper maintenance. The creaking floors might be part of the story of how the house has aged and been used.