Anisotropy in general refers to 3 axes of variance (lets say light) and is largely due to the crystal structure on the material. A isotroptic generally refers no difference in the properties due to the crystal structure (e.g. salt, diamond). A tranverse isotropic in general refers to 1 axis being different from the other two. For example the X-Y velocity of light/sound is similar in 2 directions but different in the Z direction.
You can find examples of this with a microscope.
If you are referring to geophysics you will also see examples of this as a result of the stress field within the subsurface and the minerology.