It is group of people that follows a basic caste system based on the 4 playing card faces. The order starts with clubs at the lowest, then hearts, then spades, and Diamonds is the highest ranking of aristocracy. People part of the Ivyclan are not born into their class, but are placed into it depending on either their personality or their standing relationship with someone of a different class. For instance, Joe is considered a clover, but because he is married to Jane, who is a heart, he is also considered a heart. The Ivyclan does get more complex, but most information on it is highly classified and only allowed to be shared between members of the Ivyclan, so no fully proper definition can be provided, other than what is found here.
Zach inducted his good friend into Ivyclan as a Club.
Bekah is technically a Club in Ivyclan, but because she is married to the King of Hearts, she is the Queen of Hearts in Ivyclan.