a) I think of "character concept" as something of an elevator-pitch for the character. As in the most detailed description I can give in one or two sentences.

b) I'd say a good character concept is one that offers a lot of potential material to work with. Not just for the GM, for me playing the character as well. If I can offer material for the other PCs to play off of too, so much the better.

c) Based on my answer for b), I'd say it does. On setting I'd add that if your character concept can be used to call attention to the nature of the world, it can make the overall gaming experience that much more memorable. And of course, some systems don't really support certain character concepts so well.