a phase

When you drop ice into water you can see two regions that are the same chemically (both H2O) yet clearly different, solid and liquid, with a sharp boundary between them. Each of those uniform regions is a phase. In materials, a phase is a region that is uniform throughout in both its structure (atomic arrangement) and its composition, and is separated from other phases by a definite boundary.

More precisely, a phase is a portion of matter with a single, homogeneous atomic arrangement and chemistry. Ice, liquid water, and steam are three phases of one substance, same formula, different structure or state. A single substance can also have several solid phases (this is polymorphism): pure iron is body-centered-cubic at room temperature (called ferrite) but face-centered-cubic when hot (austenite), same atoms, two different crystalline phases. In alloys, several solid phases of different composition and structure can coexist, each a distinct region.

Phases matter because a material's properties often depend on which phases are present, how much of each, and how they are arranged (the microstructure). Steel is hard or soft largely according to its mix of phases. A phase is not the same as a grain: one phase can be split into many grains (crystals of the same phase, differently oriented), while one grain is always a single phase. Caveat: the boundary that defines a phase is a real interface across which structure or composition jumps, not merely a change in shape.