TheSamnite House at Herculaneum was built a century (give or take a couple decades; it’s usually dated as 2nd century BC) before the Romans claimed the town (89 BC), when it was still under control of the Italic tribe of Samnites - hence the name of the site.
The house seems to follow vaguely the traditional, simple, axial plan of domus italica (bottom left picture), even simplifying it a bit. It also sticks to the Italic tradition according to which the atrium - the central hall with an opening in the roof (compluvium) and a drain pool (impluvium) below it - was the most important room of the house. The interior decoration, however, is a whole different story.
2nd century BC was the period when Hellenistic architecture began to strongly influence the Italic tribes… and suddenly everybody wanted to have columns and pilasters in their houses. The most common ways of including them was by adding a peristyle (an inner courtyard surrounded by a colonnade, which was an important feature of Greek houses) or by building a tetrastyle atrium, with four columns surrounding the impluvium, like in the atrium of Villa San Marco at Stabiae (bottom right). The owner of the Samnite House, however, took a different route. The atrium is more elevated than usually. This allows for a second story with a blind colonnade, which on the wall opposite to the entrance turns into an open gallery. So there you have it: a paradox, a traditional room whose traditional importance was emphasized with untraditional means.
The Samnite House is also know for its decoration in the First Pompeian Style (aka masonry style or incrustation style) which was a result of Hellennistic influences. The wall paintings of this style were supposed to give an illusion of a wall richly decorated with marble and other expensive stones.
More info on the Samnite House in this Yale lecture by Diana E. E. Kleiner.
More on Pompeian Styles in painting from the Met’s Heilbrunn Timeline of Art History.
Picture sources: Dave & Margie Hill/Kleerup (x, x,) on Flickr, Richard Mortel (x, x, x) on Flickr, Mentnafunangann (x,x) on Wikimedia Commons, Tobias Langhammer on Wikimedia Commons.