I'm sure there are other capable individuals around who could offer their 2 cents....but I'll offer mine since you asked.
Shorter:
Big achievement if it works, and a long time in the making. By concentrating a lot of energy in a small space, you can generate an explosion that will compress a small amount of fuel - causing nuclear fusion. The neat part is that this method won't require nearly as much energy as past methods - which means that this method might be able to be used in energy applications (making more energy than is put in). There will be some serious engineering challenges, though, that could mean that this great science experiment may not be able to be used in large-scale energy production in an efficient manner.
Longer:
The term "man-made star" is a marketing concept and the idea isn't all that new. It isn't the first man-made star...that honor would be bestowed upon the thermonuclear weapon. Nonetheless, it will be a significant achievement. Up to now, fusion scientists have tried to use absolutely massive magnetic fields (that consume unbelievable amounts of energy) to create fusion. This is great - but it is hard to imagine parlaying this into anything energy efficient.
This is where laser technology comes in. As far as streams of energy go, it's hard to get more efficient than a laser. So, with the use of lenses, you can efficiently concentrate a high amount of energy into a very small area (as they said in the article, the fuel here is the size of a PINHEAD). So, yeah....they are going to create a ultra-miniature man-made star that will last for a fraction of a second. The cool part is that in doing so, they hope to not expend all that much energy...a key for using this process in the future for energy production. What I am not sure at this point is how they plan to harness the energy. I would imagine that you could use a series of flowing loops that would allow for heat transfer from the outer reaction chamber to something like a steam turbine. The problem with this is that you lose massive amounts of energy in this transfer I would think. I suppose that this is a significant remaining engineering challenge (how do we efficiently capture this energy - perhaps the biggest question once we prove we can produce fusion with lasers).
What I find most interesting is that in many, many ways this research is following the process of creating a miniature thermonuclear weapon - with the absence of a lot of the radioactive components. The original plutonium-design atomic bomb relied on carefully placed explosives to simultaneously explode and compress the nuclear fuel to generate the nuclear blast - this was not a "man-made star" because it was a fission device. Now...to the fusion weapon....If you accept the common understanding of the Ulam-Teller weapon design, then this fission device is used to create massive amounts of energy in the form of X-rays (just as in this fusion research) can be focused to create a secondary fusion reaction caused - just like this case - compression of fusible fuel. The designs are different because in the weapon you want more and more neutrons to be released to cause an uncontrollable reaction - so you use something like tritium. In this case, you want a more controlled fusion reaction, so you wouldn't use such an unstable fuel (or at least, I would think that you wouldn't). I'm not a physicist...so maybe someone can correct me.