From measurements on gases.
Pressure and volume are directly proportional to temperature, but there is an offset. For any gas, the pressure and volume would be zero at a temperature of about -273.15°. (In actual fact, all real gases liquefy at higher temperatures. But because the graph is a straight line, we can extend it. Also, a gas could never have zero volume; because even as a solid, the particles of which it is made would take up some space. However, in most gases, the volume of the particles is negligible compared to the volume of the container. Gases also tend to liquefy at very high pressures, because higher pressure means more particles and the volume of the particles becomes appreciable.)
Kinetic theory says that temperature is due to the particles in a substance bouncing around: the hotter it is, the greater the vibration. This explains many phenomena, including the pressure of gases, the behaviour of liquids and solids, heat transfer by conduction, the fact that heating speeds up chemical reactions (particles can only react when they collide into one another with sufficient energy) and thermal noise in electronic components. Absolute Zero is the temperature at which particles do not vibrate at all.
It's not possible to realise such a temperature in practice because the colder something is, the faster it heats up. Even deep space is a few degrees hotter than absolute zero, just from the few stray particles that are floating about picking up radiant heat from stars. And even if you did, no thermometer would work!
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