The speed of light is about 300 million meters per second, or 186,000 miles per second. That's insanely fast, and yet the unit of measurement for our galaxy is the light year- about 6 trillion miles (yes, the light year, like the parsec, is a measure of distance, not time). Our closest star, besides the sun, is Alpha Centauri, and it's about 4 light years away from us. Potentially habitable planets may be hundreds or even thousands of light years away. Which means, if it's possible to break the speed of light, we definitely should. Unfortunately, science says right now that the speed of light is an interstellar speed limit, and if we were to break it, there would be severe fallout (like mass becoming infinite, which could instantly collapse the universe). Scientists and science fiction authors have worked on ways of subverting the rules for years, but with little hope for success. So when I heard about scientists already doing it, and ten years ago to boot, I was excited, but skeptical- this is the sort of thing that would revolutionize text books, and I hadn't heard anything about it.
Unfortunately, it's a matter of conflating two distinct but important principles in physics. The speed of light that I mentioned above is actually the speed of light in a vacuum- in other words, if there is nothing to impede lights' travel, that is how fast it will go. As soon as it hits a substance, such as our atmosphere, or water, it slows down. This is nothing new. Any kid with a clear drinking glass can demonstrate this phenomenon by sticking his finger into the water- it appears to bend in an unusual way. The light is traveling at different speeds through the different mediums.
So, what am I saying, the speed of light isn't constant? You bet. It slows down all the time. Then, what does c stand for in the famous equation E=mc^2? The speed of light in vacuum. This refers to a particular behavior of light, and while we can make objects without mass that can momentarily exceed it through quantum tunneling or particularly odd patterns of bending, c has yet to be exceeded in any meaningful way. The occasions when we have been able to get light to exceed c are either done through technicalities, such as by sending random bits of light forward and some backwards, or only occur over a few feet.
This article refers to one of these technicalities. To help get your head around exactly what's happening, consider this: two ice skaters doing laps side by side around an oval track. At the far end of the track, the inside skater grabs her team mate and pivots, flinging her partner forward much faster than either of them could do on their own. When light hits certain mediums, the waves get squished together, some will slow or even go backwards and others will be flung forward. The effect is short-lived, and doesn't hold much promise yet for any practical purposes, but who knows what the future will hold?
So the take away is this: when you refer to the speed of light, remember that you're usually referring to the speed of light in a perfect vacuum.