phase coexistence
Drop an ice cube into a glass of water and let it sit so it neither melts nor grows. The ice and the water are not fighting; they have reached a stable standoff, sitting side by side indefinitely. That settled side-by-side state — two (or more) phases together, neither one taking over — is phase coexistence.
Coexistence is a balance, not a freeze-frame. Molecules constantly cross from solid to liquid and back, but at exactly the same rate, so the amounts hold steady. The deep condition that makes this possible is that each substance has the same chemical potential — the same per-molecule escaping tendency — in both phases. When the potentials match, neither phase has any net pull on the other, and they coexist in true equilibrium.
Phase coexistence is the physical meaning of every line and point on a phase diagram: those features mark exactly the temperature-and-pressure conditions where phases balance. It is also why a boiling pot or melting ice stays pinned at one temperature — the system is locked onto a coexistence condition until one phase is used up. Distillation, freezing-out of crystals, and even clouds forming all rest on this balance.
A slush of ice and water in an insulated cup holds rock-steady at 0 °C: as long as both ice and liquid are present, the temperature cannot move, because the two phases are pinned in coexistence.
While two phases coexist, the temperature stays locked.
The condition for coexistence is equal chemical potential of each component in every phase — a deeper statement than 'equal temperature and pressure,' which alone don't guarantee balance. This equality is exactly what the phase boundary lines on a diagram trace out.