Basin of Vows is a Dark Souls III Key Item
You can use the Basin of Vows at the Cathedral in order to go to Lothric Castle. This will trigger the appearance of the area’s first boss, the Dancer of the Boreal Valley.
You can opt to kill Emma or not, the choice makes it so that there is more than one way to obtain this item.
The Basin of Vows is a chalice used by the Lothric Knights when they receive their Knighthood and take their vows.
This tradition is just a simple formality as of now, but the tradition carries on.