I was about to sarcastially ask
What problem does it solve? as the Beeb article was unenlightening (nice pun
)..
Then I remembered the fact that just sometimes (ie nearly always) the Beeb's technology articles completely miss the point. So I did a quick search...
As pointed out in wikipedia, it has advantages in electromagnetically sensitive environments, such as aircraft and some areas of hospitals, where WiFi would be unwelcome. Which makes it much more interesting, IMHO.
http://en.wikipedia.org/wiki/Li-Fi