State of Matter
A state of matter is one of the physical forms matter can take, mainly solid, liquid, gas, and plasma, based on how its particles move and are arranged.
Definition
A state of matter is the physical form a substance takes: solid, liquid, gas, or the fourth state, plasma, and which one a substance is in depends on the arrangement and motion of its particles. In a solid, particles vibrate in fixed positions, giving definite shape and volume; in a liquid, particles slide past each other, giving definite volume but no definite shape; and in a gas, particles move freely and fill any container, while plasma is an ionized gas with free electrons. More formally, states are distinguished by the balance between particle kinetic energy and the intermolecular forces attracting them, and by their order, since crystalline solids have long-range order, liquids have only short-range order, and gases have none; a phase diagram maps the stable state as a function of temperature and pressure, with a triple point where solid, liquid, and gas all meet and a critical point beyond which liquid and gas become indistinguishable.
Example
Ice is water as a solid, drinking water is a liquid, and steam is water as a gas, the same molecules just arranged differently, and at $-10^\circ\text{C}$ water is rigid, at $20^\circ\text{C}$ it flows to fit a glass, and at $110^\circ\text{C}$ it becomes an invisible gas that spreads through a room. Water's triple point sits at $0.01^\circ\text{C}$ and $611\text{ Pa}$, and its critical point at $374^\circ\text{C}$ and $22.1\text{ MPa}$; above that critical point, supercritical water dissolves organic compounds like a solvent while flowing like a gas, and supercritical $CO_2$, above $31^\circ\text{C}$ and $7.4\text{ MPa}$, is used industrially to decaffeinate coffee.
Key Insight
The state a substance is in depends on how fast its particles are moving: heating spreads them out and cooling packs them together, and gases compress easily because their particles are far apart while liquids and solids barely compress since their particles already touch. Glass is often called a solid, but it is really an amorphous material with the disordered structure of a liquid frozen in place, and whether that counts as a genuinely distinct state remains an open question, a reminder that "three states" is a simplification.