The mansion is the home of Edna Mode and where she does her work for Supers in the "glory days": they would of come to her home to get, reaper, update and see how their suits turned out and work with their powers.
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 had 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 and Edna showed her the (matching) suits that she had made for her and her children in her high-tech design studio.