Colonel Pyncheon makes it a condition in his will that his portrait cannot be removed from the parlor wall of the House of the Seven Gables. This portrait makes it impossible for any of his descendants to forget either (a) the Matthew Maule story, since that story is connected to Colonel Pyncheon, or (b) the "evil influence" or "Evil Genius" (1.27) that continues to cast its power over the Pyncheon family line. Colonel Pyncheon's stern, cruel face makes it totally clear for all onlookers exactly what lurks in the hearts of the Pyncheon family. The portrait becomes a touchstone for everything bad in the Pyncheons. (It also apparently shakes its head or frowns when something it doesn't approve of happens to the Pyncheons, which is not a pleasant trait for a painting outside of Hogwarts, we think.)
By the end of the novel, we discover that the long-lost secret to the Pyncheon family fortune has been lying in the wall behind Colonel Pyncheon's portrait all along. It was left there in revenge by Thomas Maule, Matthew Maule's son. If Colonel Pyncheon hadn't insisted that no one could ever move his portrait, maybe the deed would have been found in time to be worth something. But his pride has shot him in the foot.