A phase transition is a transformation from one state (i.e., phase) of matter to another, e.g., solid, liquid, gas, or plasma.
The states/phases are regions within temperature/pressure-space within which a material obeys normal-looking equations, such as the ideal gas law. A phase transition is where an abrupt change takes place, requiring different but analogous equations. They are associated with an abrupt change in the amount of energy being tied up in the material, e.g., the latent heat in liquid water as opposed to ice, or in steam as opposed to liquid water.
The term phase transition is also used in physical sciences for other situations that have an analogous abrupt changes not simply handled by a typical equation.