Here's my attempt to explain the 'torque' bit - apologies in advance if it's at the wrong level. I work in the applied physics field involving spin torque (spintronics) and I have an enthusiast's basic knowledge of computer tech, but those two aspects are quite far apart in my head.
The torque being referred to is a magnetic torque - when an electrical current passes through a magnetic material, it gets 'spin-polarised'. You need to look into the physics of electrons a bit to understand that, but basically it means that a current coming out of a thin film magnet and into another thin film magnet exerts a magnetic torque on the second thin film.
As in magnetic hard drives, this type of storage is based on measuring the electrical resistance of one bit of storage, and the way that is done is by changing the direction that the magnetism of two layers points. If they point in the same direction, it is a low resistance state. Conversely, opposite directions mean high resistance - those are your 0 and 1 states right there.
The trick is how to change the orientation from 1 to 0 as you need for writing. You can use a magnetic field from outside, but that isn't too efficient and risks you switching the orientation of other bits than just the one you want. However, with this magnetic (or spin) torque, passing a current directly through the first magnetic layer lets you change the magnetic orientation of the second layer without a magnetic field at all. This won't affect any other bits around the one you're changing, and the smaller you make the bits, the less power this whole process takes.
FWIW, this is the WikiPedia article on spin-transfer torque, though it's pretty technical.
http://en.wikipedia.org/wiki/Spin-transfer_torque
For me this is quite exciting - as the article says, it has been a decade or so since this type of storage was first promised. It's always good as an experimental research physicist to point to some piece of commercial tech making some company billions and say 'that's why you should continue to fund my research'.