Although the details are still unknown, the big picture shows a straightforward system. Here's how it will work. You will be able to login with their Facebook or LinkedIn profiles when you check-in for their flight online. KLM says the service will be available to all passengers checking in online, but you will be able to choose whether or not to make your profile publicly available.
The point is to let people sit beside each other based on if they have similar interests. Chances are, however, that most people will simply judge their potential seatmates based on their profile picture(s).
Overall, it's not a bad idea, as long as it's optional. I would likely try to choose someone who is near my age, or at least looks like he or she is. At the same time though, sometimes I just want to get work done and I would rather pick someone who won't want to constantly try to engage me in conversation.
Tnooz, which first reported on the story, notes that KLM is not the first airline to consider the idea. Virgin Atlantic has also mulled allowing people with similar likes to hook up during a flight.
Malaysia Airlines has a similar service that lets you see what Facebook friends might be taking the same flight or travelling to the destination around the same time. In that case, however, the individuals already know each other.
KLM, Virgin Atlantic, and Malaysia Airlines all have fairly popular Facebook Pages. They have 600,000 Likes, 100,000 Likes, and 400,000 Likes, respectively.