The DirectX graphics system in Xbox One is a superset of Direct X 11.1 for Windows, with variations that are specific to the Xbox One console.
Xbox One has a modern, DirectX 11.1 compliant graphic processing unit (GPU), and uses Direct3D 11 for graphics presentation. The Direct3D 11 implementation on Xbox One is a superset of the Direct3D 11.1 that is available in Windows 8.
For conceptual documentation about Direct3D 11, see Direct3D 11 Graphics at MSDN.
Some items in the DirectX header files in the XDK are not actually implemented on Xbox One. If a method is declared in the XDK version of a header file, but the method isn’t actually supported on Xbox One, the method returns the error code E_NOTIMPL, meaning “Not Implemented”.
Many of the changes to Direct3D from the Windows version are because Xbox One uses a single specific hardware platform, and Game OS titles require very high graphics performance.