Proof of your problem solving skills and ability? To see that you are prepared to take ownership of a problem and see it through to a sucessful outcome? To see the way you go about tackling problems / which methods of problem solving you use?
Most employers I've encountered just want to see an instance perhaps of when you have gone above and beyond what is expected of you. Be careful though don't make it all out like it was 'your' problem to be solved as sometimes they use it to make sure you are a 'team player' as such and make sure you mention enrolling any colleagues etc to help you.
cheers all, i hate these questions as once u've solved something n some time has passed, it never seems like that much of a problem lol. it's almost as if u have to make up a scenario to show how u did some problem solving :o/