Clans are the first level of "continual grouping", if you want to think of it in that way... somewhat similar to other MMO's guilds except that the name of the clan you join, becomes your last name. A clan is just what the name implies, your "family", of sorts. Who can join a clan? Individual players.
Guilds are more similar to alliances (such as those found in DAoC), yet again, they are different. Guilds are meant to be true guilds, accepting whole families (clans), or single individuals as members. If a you belong to a clan, and the leader of that clan, makes the clan as a whole join a guild, you then are part of that guild, and in order not to be associated with that guild, you must leave your clan.
Great Houses are the three factions: Kinnaes, Arcanum & Gear. At this time it is not understood if any one person or guild will control a great house, however, members of the Great Houses are made up of guilds. The three factions, or Great Houses, thus strive to control the Triumvirate. The Triumvirate oversees everything, as a ruling body of sorts, as I understand it.
Thus it is my understanding, as told to some of us by Simu staff, that clans will align with guilds which align with the three factions, or Great Houses, which then fight to control the majority of the seats of power on the Triumvirate (think ruling council). It also has not been made clear, but it's been suggested that whichever Great House occupies the majority of the Triumvirate will thus establish bonuses for any players aligned with said faction/Great House. This was possibly suggested by other players, or hinted at by GM's, I do not recall... so take it as it is given, a possibility and in no way fact.
Clans names will be your last name, Guilds will be displayed in some form as a title, and not sure if your faction/Great House is also displayed.
Hope that helps...
~ Jaraeth