Wiktionary
n. (context physics English) The dependence of any magnetic property of a material on the direction in which it is measured.
Wikipedia
Magnetic anisotropy is the directional dependence of a material's magnetic properties. The magnetic moment of magnetically anisotropic materials will tend to align with an "easy axis", which is an energetically favorable direction of spontaneous magnetization. The two opposite directions along an easy axis are usually equivalent, and the actual direction of magnetization can be along either of them (see spontaneous symmetry breaking).
In contrast, a magnetically isotropic material has no preferential direction for its magnetic moment unless there is an applied magnetic field.
Magnetic anisotropy is a prerequisite for hysteresis in ferromagnets: without it, a ferromagnet is superparamagnetic.