The Fifty Families are the current ruling houses of Europa. Many of them are Sparky lineages, but some of them are just old-fashioned royalty. Many Spark lineages are considered seperate from royalty like the House Mongfish. They do not much like Klaus's rule over them, but can't do anything about it, at least openly.
They have strict rules and social taboos against resurrection. Revived individuals are apparently removed from lines of succession.
The Storm King conspiracy references the Fifty Families, claiming that their Storm King is one that the Families will officially recognize (mostly because he will restore their power). Whether this means that the Families are actively involved in the conspiracy or simply a predictable element is unclear.
Agatha H. and the Clockwork Princess reveals in a poem that every one of the families wants to have one of their own recognized as Storm King.