This is some seriously big news. Jack the Ripper is one of the most notorious serial killers and he has so many legends because no one knew who he was. Of course, let me point out the quotes around the word prove. What the test really proved was Aaron Kosminski had contact with a Jack the Ripper victim. It doesn't actually mean that, yes, without a doubt, he was Jack the Ripper.
Another thing that has me excited about this development is a book I have called The Cases That Haunt Us by John Douglas and Mark Olshaker. If you don't know, John Douglas is one of the men who helped develop profiling. He's an expert. In the book, he talks about the suspects for Jack the Ripper and Aaron Kosminski is one. In fact, John Douglas said Aaron Kosminski fit his profile, but there were a few things that made him think Aaron Kosminski wasn't Jack the Ripper. (His other possible choice was a man named David Cohen. He ends the chapter by saying: Therefore, I'm not prepared to say that Jack the Ripper was either the man known to police as David Cohen... or someone very much like him.)
The DNA test doesn't really close the case on Jack the Ripper. If anything, we now have an exciting new chapter. But to say we know who Jack the Ripper is would be speaking too soon. In reality, we may never know without a doubt who he was. He may have been Aaron Kosminski or he may have been David Cohen or he may have been someone else. One thing I do know, Ripperologists are probably having a field day.
*Edited to add: John Douglas' coauthor, Mark Olshaker has weighed in on this at their website, Mindhunters.