This article from MIT talks about the applications of slowing down light so that electrons can actually move faster than it. This creates an optical boom, which means that electrons can move ridiculously fast in a particular medium (graphene, an atom-thick form of carbon). This could speed up computers by six orders of magnitude, meaning that computers will be able to run 6 times faster.
Obviously, this has numerous applications. The fastest computer on the planet, right now, can perform 93 petaflops; that is, it can do 9.3e16 floating-point operations every second. Now, imagine a computer that can do 9.3e19 operations each second! With that, you could build the hardware necessary for a sci-fi-level Artificial Super Intelligence!
That's what is possible with this technology.