Prior to the events of S5E8, Griffonstone fell into disrepair after the loss of the Idol of Boreas. It's slowly on its way back to a proud Griffon enclave, helped along by Gilda and her efforts to spread friendship.
Griffonstone isn't located in the Griffonlands, residing instead upon the eastern coast and border of the Equestrian continent and nation, respectively.
Griffonstone was founded after the natural greed of Griffons led to civil unrest in the Griffonlands, and a group of refugees established the kingdom after crossing the ocean between Equestria and the Griffonlands. These refugees were loyal to the once-emperor of the Griffonlands.