anisotropic distribution

Anisotropic distributions are those that are not isotropic.

Informally this means that the variance is not the same in all directions—the distribution is not rotationally invariant. Perhaps the covariance matrix defines an ellipsoid instead of a sphere, for example.

Mathematically, the definition is that $P$ is anisotropic if there exists some orthogonal matrix $Q$ such that

$$X\ne QX,$$

in distribution, where $X\sim P$. This is simply the negation of the anisotropic condition. Thinking about it intuitively is much easier.