Temperature is a measure of the average internal energy of an object or a system.
Internal energy is energy associated with motion of atoms and/or molecules.
Temperature is therefore a measure of the average kinetic energy of the atoms and molecules making up an object or a system.
Several physics formulas involving temperature only make sense when an absolute temperature is used.
Rule of thumb: if an equation involves T, use a temperature in Kelvin. If an equation involves ΔT, Celsius or Kelvin is fine.
A device used to measure temperature is called a thermometer, and all thermometers exploit the fact that properties of a material depend on temperature. Examples of temperature-dependent properties include:
All these effects, and plenty of others, can be used in thermometers.
A sealed container of gas can give us a good idea of what absolute zero is all about. The volume of gas inside is essentially constant, and measurements show that the pressure of the gas is directly proportional to the temperature. At some temperature, the pressure is going to read zero - this temperature is absolute zero.