The "Generalidad" is the Spanish term for "la Generalitat", which is the Catalan name for the Autonomous Government there.

Here's what the "Generalitat" has to say about itself on its website (cited below):

The Generalitat is the institution in which the self-government of Catalonia is politically organised. It consists of the Parliament, the President of the Generalitat and the Executive Council or Government of Catalonia. Here you can find everything you might want to know about the role, responsibilities, organization, economic resources, and historical origins of the institutions and offices of the Generalitat.