I can't play youtubes, but read the first body paragraph of this wiki and tell me you know what it means. I'm a high-amateur physicist and it's gibberish to me.
The concept seems pretty simple, its basically just magnetic pumping of heat in an odd ball (magnetocaloric) material. Reversal of the magnetic field applied to this material create a bi-directional thermal movement as the domains are re-orientated in an alternating pattern.
The first question is what is the availability/cost of Gadolinium or other suitable magnetocaloric materials? Also how much of this material would be needed to provide usable cooling? Finally brass tacks, how many BTU's per watt are we talking? I realize its early yet but somehow I'm not holding my breath on this technology.
It reminds me a bit when they started playing with the Peltier effect using semi-conductors. Apart from a few specialized small heat transfer jobs, like cooling CCD camera sensors, their marked inefficiency means they will never replace compression cycle refrigeration.
The "coolest" (sorry) use of Peltier cooling was the AGV refrigerated motorcycle helmet. There is a fluid filled bladder that rests on the users head and the junction pumps heat into the mohawk-style heatsink on the top. Reversing the current applies heat to the users head! "I Pity the fool, that can't keep their cool" possible Mr "T" celebrity endorsement...