Faufreluches was a term commonly used to describe the class system employed during the days of the Old Imperium.
The faufreluche system was meant to provide some sort of order for the way in which humanity related with one another, both to maintain order and civility, and to keep certain groups under control within the Imperium. However, it attempted to minimise alienation of individuals or minorities by providing for everyone: The motto of the faufreluche system was "A place for every man and every man in his place."
The theory behind the Faufreluche system's existence was that, because of the vastness of the universe, and the immense distances across which humanity was scattered, a central figure—the Emperor—was required to provide focus and direction in people's lives. This figure was represented locally for people by the head of the Great House that governed them. 
Flaws in the Faufreluche system could be seen in that House Harkonnen, once banished for cowardice after the Battle of Corrin, could return and become a viable political power through market manipulation.
Moreover, the prescient powers of Paul, Alia, Ghanima, and Leto Atreides II revealed that the scattering of humanity without central leadership was precisely what was required in order to save it from stagnation, and, eventually, annihilation; if the entirety of humanity was concentrated sufficiently to be ruled by a single interest, it was likewise vulnerable to destruction by a single threat. Thus, upon Leto II's death, the Faufreluche system effectively ended, and humanity exploded across the universe in an immense Scattering, ensuring humanity's future would be secure.
Behind the Scenes
Despite the re-emergence of Great Houses after The Scattering in Heretics of Dune (novel), it does not appear that the Faufreluche system was recreated. These re-emerging Great Houses appeared to be simply one faction of an entirely fragmented society, with many powerbrokers, with none seemingly more powerful than another.
The Faufreluche system is heavily based on the Mamluks of the ancient Ottoman Empire. The Mamluks were slave soldiers who converted to Islam and served the Muslim caliphs and the Ayyubid sultans during the Middle Ages. Over time they became a powerful military caste.
The Mamluk system gave rulers troops who had no link to any established power structure. Parallels can be seen with the Faufreluche system here. The local warriors were often more loyal to their own nobles rather than the monarch (similar to the fact that subjects of the Great Houses were typically more loyal to their Household leader rather than the Padishah Emperor in the Faufreluche system).
If some nobleman conspired against the ruler, it was often not possible to deal with him without causing unrest among the nobility. In much the same way, The Padishah Emperor could not openly destroy a Great House without invoking the combined power of the Landsraad. This is why Emperor Shaddam Corrino IV had to conspire against House Atreides in secret.
Sultans had the largest number of Mamluks, but the other amirs could have their own troops as well. Many Mamluks rose to high positions throughout the empire, including army command. Over time in places like Egypt the Mamluk forces became linked to existing power structures and gained significant amounts of influence on those powers. Eventually they rebelled and established a sultanate of their own in Egypt. Again, in much the same way, House Atreides developed a strong powerbase through the Faufreluche system, and eventually become the new imperial dynasty.