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."
An integral part of the Faufreluche system were the Great Houses, Minor Houses, siridar fiefs, and the Padishah Emperor. 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 during the The Golden Path, ensuring humanity's future would be secure.
Behind the Scenes
Despite the re-emergence of Great Houses after the Scattering in Heretics of Dune, it does not appear that the Faufreluche system was re-established. These re-emerging Great Houses appeared to be simply one faction of a fragmented society, with many powerbrokers, with none seemingly more powerful than another.
While much of Dune was based on Arabic concepts, the Faufreluches system is clearly based on feudal European concepts, especially that of the mid-period Holy Roman Empire, an elective monarchy. This kingdom was ruled by an Emperor, typically heir of the most powerful state within the Empire, which was mostly the Hohenstaufens or Habsburgs during this period. The Emperor was not automatically the father of the next Emperor and could be replaced, much like the Habsburgs replaced the previous dynasties and the Atreides replaced the Corrinos.
Below the Emperor were very powerful princes and dukes who basically ran de facto independent autonomous states. They each had their own dynasties, much like the Great Houses of Dune. The most powerful states were the Electoral States, whose power relative to the Emperor was very much like that of the Atreides and Harkonnens against the Padishah Emperor. Alongside them but not subject to the rule of the great states, were minor ones, though often reliant on their protection, aka the Minor Houses and siridar fiefs.
A feudal subject's allegiance was to his lord, not directly to the Emperor. Many wars would be fought against the Emperor who may have been very powerful in his own right but could not fight the entire Empire, just like the Landsraad could oppose the Emperor if united. The Imperial Diet is quite clearly the inspiration of the Landsraad. The Landfrieden of the Holy Roman Empire (limiting the right of violence and feuding) is an example of another analogue with it being translated into Dune as Kanly and War of Assassins.
Alongside the Emperor, major states and minor ones, there existed powerful power structures, chief of them the Church (a weak analogue of the Bene Gesserit) and powerful guilds running independent systems and cities (an analogue to the Spacing Guild).
The Emperor did not have an elite army analogue to the Sardaukar, though he would have the theoretical ability to call the Army of the Holy Roman Empire from his feudal subjects. The Sardaukar seem to be heavily based on the Janissaries or Mamluks of the ancient Ottoman Empire.
The Holy Roman Emperor spent much of his time and effort keeping a delicate balance of power between the Electoral States, who were also very careful not to be subdued by the Emperor, leading to divisions and fragmentation which would doom the Empire in the future. The Holy Roman Empire was eventually destroyed by Napoleon, who while being of low noble birth, was a charismatic military genius and adventurer who crowned himself Emperor, while having a beloved consort in Josephine but having to eventually marry the daughter of the Austrian Emperor (the last Holy Roman Emperor, who had abdicated his position after zealous French revolutionary armies swept the old Empire), another analogue in Dune.