The term phase transition was first used in physics to describe changes in states of matter. The states in question being, of course, gases, liquids and solids. By extension it is used in thermodynamics to describe a sudden change in one of the parameters describing the state (in the thermodynamic meaning of the term) of an arbitrary system (often specific heat).
Thus the transition from the ferromagnetic to the paramagnetic state, the appearance of superfluidity or a change in the type of crystal lattice are all called phase transitions.
There is a very wide and highly complex theory to try to describe these phenomena from the renormalisation group in statistical physics.
The phenomenon is very general and applies both to material systems and to fields of interactions.