Absolute zero is the point where no more heat can be removed from a system, according to the absolute or thermodynamic temperature scale. This corresponds to 0 K or -273.15°C. In classical kinetic theory, there should be no movement of individual molecules at absolute zero, but experimental evidences shows this isn't the case.
Temperature is used to describe how hot or cold an object it. The temperature of an object depends on how fast its atoms and molecules oscillate. At absolute zero, these oscillations are the slowest they can possibly be. Even at absolute zero, the motion doesn't completely stop.
It's not possible to reach absolute zero, though scientists have approached it. The NIST achieved a record cold temperature of 700 nK (billionths of a Kelvin) in 1994. MIT researchers set a new record of 0.45 nK in 2003.
Sources:
http://chemistry.about.com/od/chemistryfaqs/f/absolutezero.htm
http://www.cartage.org.lb/en/themes/Sciences/Physics/Cryogenics/AbsoluteZero/absolutezero/AbsoluteZero.jpg