Anisotropy is a bias in the direction of lighting a surface. At 0 % a surface is isotropic, meaning there's no bias. As you approach 100 % your surface will become maximally anisotropic. Some degree of Roughness is necessary for anisotropy to be visible, and the amount tells the anisotropic highlight how far to "spread".
Anisotropy requires that there is a Projection node input otherwise you will get strange polygonal shapes in the render.
Left: Anisotropy at 100 %, Rotation at 15 %, Roughness at 30 %. Right: No Projection
This determines the angular rotation for your anisotropic highlights. At 0 % the rotation will follow the curve of your object and at 50 % will be perpendicular to it.