The Elder Scrolls V: Skyrim – ‘The Claw’ Door Combination

It is the Dark Brotherhood's sanctuary.

To get through that door you have to

kill the owner of the orphanage in Riften and then a courier brings you a note. Sleep to be contacted by them, then they will give you the necessary information to join from there.

They may not contact you the first time you sleep so keep trying, eventually they will.

Spoiler:

Go back to the inn with the guy's diary and talk to the innkeeper. He'll give you a sapphire claw as payment. You then use it identically to the one you use in Bleak Falls. If you haven't started the quest, pretty sure you can just talk to the innkeeper anyway and start it, then immediately fork over the diary to get the claw.