We define temperature as a measure of the average kinetic energy of the particles that make up our sample. Kinetic energy is the energy that something has because of its movement: the faster it goes, the more kinetic energy it has.
In materials with fast particles, the atoms and molecules are just zooming around, bouncing off each other and everything else. This high energy material we call "gas" or, if it is really energetic and full of ions, "plasma".
Slow everything down and stuff sticks together. This we call a liquid. Slow it down even further, and we have a solid.
Notice that we are slowing stuff down. What is happening to our kinetic energy? It's getting lower. And the temperature? It's getting lower, too (Remember temperature and average kinetic energy are related).
Now, what is the slowest speed that anything can go? Standing still! If it goes backwards, it is still moving so it will have a speed. At the point where everything stands still, the kinetic energy will be zero, just like the speed. And the temperature will be zero, too, since the average kinetic energy of all of these now motionless particles is zero, too.
Theory states that we can get really, really close to Absolute Zero (the 0 point on the Kelvin scale), but never reach it. This has to do with all kinds of things, including the fact that you can't stop electrons from orbiting around the nucleus, etc.