The Cycles Tangent node defines a Tangent-Space for a mesh by either using one of the object’s local axes or by using an available UV layout.
This can be useful when designing an Anisotropic reflection shader like in the case of brushed, machined or lathed metals.
In the first example the Tangent node is set to ‘Radial’ Direction mode, in which a object axis is chosen as the radial axis of the Anisotropic direction.
In the second example the Tangent node is set to ‘UV map’ Direction mode, in which a UV map is chosen as the Anisotropic direction.
In order to create a special Anisotropic direction you would usually not create a deformed UV layout, but a normal one, and connect a grey-scale texture to the Rotation input of the shader to define changes in the Anisotropic direction on the surface.