temperature
Temperature is what a thermometer reads, and what your hand feels as hot or cold. At the everyday level it tells you which way heat will flow: touch a hot mug and warmth flows into your skin; hold an ice cube and heat flows out of you into it. Heat always drifts from the warmer thing to the cooler one until both reach the same temperature.
Underneath, temperature is a measure of the average random motion of a substance's particles. The hotter something is, the more vigorously its atoms and molecules jiggle, vibrate, and fly about. Temperature is an intensive property — a cupful and a bathtub of the same warm water read the same — and it is precisely the quantity that becomes equal when two things reach thermal equilibrium.
It matters because temperature controls almost everything in physical chemistry: how fast reactions go, which way they shift, what state a substance takes, and how gases press on their walls. The deepest scale, the absolute or Kelvin scale, starts at absolute zero, the point where particle motion is reduced to its irreducible minimum and no heat can be coaxed out of a body.
Drop a hot spoon into cold soup and you feel the spoon cool and the soup warm until they meet in the middle — that shared final reading is the temperature they both reach.
Temperature is the quantity two touching objects equalise as heat flows between them.
Temperature is not the same as heat: temperature measures how hot something is, while heat is the energy that flows because of a temperature difference. A small spark can be far hotter than a warm bath yet carry far less heat.