A cutscene plays, and you’re transported to, duh duh dunnnnn… the Kiln of the First Flame. Once you’ve put Lothric’s head on his throne the Fire Keeper will walk towards the bonfire at the centre of the Shrine and you’ll get an interaction prompt there.
To get to the end fight you need to have killed all of the other Lords of Cinder – which includes your little pal Ludleth, by the way, although you’ll be happy to know that you can still transpose souls into weapons at his throne even after he’s gone. It’s another cheat-y sort of fight, but it’s probably not the hardest you’ve had to face.
It’s also the gnarly cover-boy for the game, and features in most of the promo material.
The Soul of Cinder is the collected souls of everyone who has linked the flame throughout the history of Dark Souls, starting with Gwyn, and including the player character from the first game. Everything in Dark Souls 3 has been working up to this moment.