After mistakenly giving two passengers the same boarding pass, thereby allocating them the same seat (a physical impossibility), it became clear as they introduced themselves to the flight attendants that both unfortunate passengers had exactly the same name - first and last. It wasn't a particularly common name, but it was a coincidence.
As the aircraft was entirely full, there was nowhere for one of the two same-named passengers to sit, so it delayed the flight for around 20 minutes as flight attendants and the second passenger walked up and down the aisles looking a bit stressed.
It's an example of the sort of thing that can go wrong when the only identifier you have for telling people apart is their name. The airline (or whoever printed up that second boarding pass for that "same" person) suffered from one of the two causes of problems NicNames aims to prevent: assuming two dealings with people with the same name mean they are the same person.
The two passengers presumably had a booking reference number, in addition to their name, to identify themselves to check-in staff (or machines). Presumably the mistake happened when someone looked up the second passenger by name, and found the other passenger's record, already with an allocated seat. They then went on to fill every other seat in the aircraft.
I don't know what happened to the extra passenger in the end - whether he got a free upgrade to business class, or was kicked off the plane. However, a similarity can be drawn to the experience of searching through citations in a repository only to find two people's work muddled in together under the same author heading.