The Independent Clans are those major clans that claim descent from Caine but are not part of either the Camarilla or Sabbat. The five clans are the Daughters of Cacophany, Giovanni, Followers of Set, Assamite and Ravnos clans.
Each clan's reason for independence varies: in the case of the Assamites and Giovanni, there are specific deals with the Camarilla that guarantee autonomy. The Followers of Set just weren't interested, and the Ravnos never participated in any party they couldn't crash first. Each clan also has certain eccentricities that seperate them from the mainstream of Cainite culture - the Followers of Set, Ravnos and Assamites all view Cainite vampires with a certain degree of disdain, and the Ravnos and Assamites are effectively tips of an iceberg. There are far more Ravnos and Assamite vampires in their home territory and their structure is more complex there, not the least of which is because of a relative lack of Cainite competition in the area. As for the Giovanni, their goals are largely insular form the rest Kindred society and they are just as happy to be left alone.