The mansion is the home of Edna Mode and where she does her work for Supers in the "glory days": they would come to her home to place an order, pick it up, get it repaired or updated, and to see how their suits turned out and how they would work with their powers. After the Supers were disowned, Edna went into the high fashion industry and continued working in her home, but for normal people.
When Bob Parr needed a "patch job" on his old suit, he turned to its designer and made a house call, but "E" called it a "hobo" suit and offered to design him a new one. Bob asked for it to have a cape, but Edna reminded him what happened to the last few supers and what their capes got them into. But she finally agreed to fix the old suit and design Mr. Incredible a new one.
Helen Parr then came up to mansion to gain some answers about her husband's suit (when she saw the patch work on it) and Edna showed her the matching suits that she had designed and made for her and her children in her high-tech design studio.
Having trouble with Jack-Jack's new powers and needed rest, Bob headed up to the mansion to see if Edna could help him. She allowed the baby to spend the night, while she makes Jack-Jack a new supersuit that could help the Parrs monitor his powers, and where he has wondered off to. When Bob returned to pick his youngest son up, Edna demonstrated the suit's "accessory" and what she had learned of the baby's powers in her design lab.