Anisotropy is the property of being directionally dependent, which implies different properties in different directions.
In computer graphics, this primarily refers to reflections on rough surfaces.
Anisotropic reflections are stretched across a surface due to a consistent orientation or pattern of roughness on that surface. Reflections blur perpendicular to the direction of repetitive grooves / fibers / scratches.
Some common real-world examples include brushed steel, hair, and optical discs.
You can find the Anisotropy panel in the Materials tab of 3D Settings. Each material in your scene can have its own Anisotropy settings. The material must have a UV map for Anisotropy to work because it requires tangents.
Intensity controls the level of anisotropic effect. The more intense the effect, the more regular and close together the (emulated) grooves are.
Direction controls the orientation of the grooves. Reflections will be blurred perpendicular to this direction. Setting a Factor for direction will set a single angle for the entire material. You can also use a Texture to define different anisotropic patterns across the material. It is sometimes called a "flow map", and uses the Red and Green channels of an image to define 2D vectors in tangent space. This is similar in concept to a normal map. You can use Swap XY to reverse the R and G channels. "Neutral blue" pixels (RGB values of [127,127,255]) will disable the effect, which means you can mask parts of a material that should not have anisotropic reflections.
Here are some examples of anisotropic textures and the result on Sketchfab.