a component
When you describe a recipe, you only list the things you actually add: flour, sugar, water. You do not list carbon, hydrogen and oxygen separately, even though those atoms are inside the flour. A component is that idea made precise for a phase diagram. It is one of the minimum number of independent chemical building blocks you need to write down the composition of every phase in the system.
The trick is minimum and independent. In the magnesia-alumina system we call the two components MgO and Al2O3, not the three elements Mg, Al and O, because once you fix how much MgO and how much Al2O3 you have, the oxygen is already accounted for — it rides along inside the oxides. So this is a two-component (binary) system. Pure water is one component (H2O) even though it exists as ice, liquid and steam. The number of components, written C, is one of the two inputs to the Gibbs phase rule; it sets how many composition knobs the system really has.
For ceramists the natural components are almost always oxides — MgO, Al2O3, SiO2, CaO, ZrO2 — because ceramic powders are batched and reactions are written in oxide terms. Choosing components well keeps a diagram as small as possible: the huge, practically important CaO-Al2O3-SiO2 world of cements, glasses and slags is a three-component (ternary) system, so its whole landscape fits on a single triangular map instead of needing every element tracked on its own axis.
Batch a spinel body from magnesia and alumina powders. Even though three elements are present (Mg, Al, O), you only need two numbers — the fraction of MgO and the fraction of Al2O3 — to specify any mixture, because oxygen is fixed inside the oxides. So C = 2, and the whole system lives on one binary diagram.
Components are the fewest independent chemicals that pin down every composition; for ceramics they are usually oxides.
Components are counted, not chosen by whim: they are the smallest set that still describes every phase. Do not confuse a component (a bookkeeping species like SiO2) with a phase (an actual region of matter like cristobalite) — a single component can appear as several phases.