I think it's great that the physics Nobel this year went for giant magnetoresistance (GMR). GMR is intrinsically a quantum mechanical effect, an example of a nanoscale technology that's made it out of the lab and into products, and one of the big reasons that you can buy a 500GB hard drive for $100. (Good job, Sujit, for the advanced pick!).
The story in brief: Back in the ancient past (that is, the 1980s), the read heads on hard drives operated based on the anisotropic magnetoresistance (AMR). For band structure reasons, the electrical resistivity of ferromagnetic metals depends a bit on the relative orientations of M, the magnetization, and J, the current density. In the common NiFe alloy permalloy, for example, the resistivity is about 2% larger when M is parallel to J than when M is perpendicular to J. To read out the bits on magnetic media, a strip of very coercible magnetic material was used, and the fringing fields from the disk media could alter the direction of that strip's M, leading to changes in the resistance that were translated into voltage changes that correspond to 1s and 0s.
In the late 1980s, Fert and Grunberg demonstrated that stacks of nanoscale layers of alternating magnetic and nonmagnetic metals had remarkable magnetoresistive properties. When the M of the FM layers are aligned, the mobile electrons can move smoothly between the layers, leading to relatively low resistance. However, when the M of the FM layers are anti-aligned, there is a mismatch between the densities of states for spin-up and spin-down electrons between anti-aligned layers. The result is enhanced scattering of spin-polarized electrons at the interfaces between the normal and FM layers. (Crudely, a spin-down electron that comes from being the majority spin in one FM layer goes through the normal metal and runs into the anti-aligned FM layer, where that spin orientation is now the minority spin - there are too few empty states available for that electron in the new FM layer, so it is likely to be reflected from the interface.) More scattering = higher resistance. The resulting GMR effect can be 10x larger than AMR, meaning that read heads based on GMR multilayers could read much smaller bits (with smaller fringing fields) for the same signal-to-noise ratio.