You will meet the Fire Keeper here and she allows your character to level up, and/or increase his/her individual attributes in exchange for a specific number of souls. Go ahead and stick the Coiled Sword into the fire pit nearby to light the bonfire here.
Check out the place some more and you'll find a shop where you can buy items using souls as your currency, as well as a Blacksmith that can take care of your gear amongst other things. That said, turn around from where Andre is and talk to the Unkindled sitting on the right staircase. He'll give you a Collapse after sharing his thoughts. By the way, it's worth going back outside and checking out the side paths near the shrine entrance for some items like Embers and another Homeward Bone. Go back to the bonfire in the shrine and travel to the High Wall of Lothric when you're ready.
Also from this point onward, you'll be able to warp back to this location from any bonfire in the world. Or by using a Homeward Bone if there's no bonfire anywhere nearby.