Normally we consider there to be three phases, or states of matter: gas, liquid and solid. In materials science, the term has an additional, rather more specialised meaning. Gas phases are of no real relevance, and we concentrate on liquid and solid phases.
There can be many solid phases, distinguished by different greek letters, the difference between them being the nature of their atomic arrangement, or crystal structure. A phase can exist over a range of temperatures and compositions, but it's atomic structure will remain the same. There may be only one gas and one liquid phase for an alloy at a given temperature and composition, but there can be many solid phases. Another way of looking at a phase is that it is a structurally distinct part of a materials system.
Associated terms: Phase Diagram, Alloy
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