Latin, actually. An exact translation is "What now?"
But its English meaning refers to gossip. A person who is a gossip constantly needs to know the latest goings-on, and that why I chose this for the town's name. Alice Williams has always lived in little Quidnunc, Indiana, and she knows the power of gossip. It can build you up or tear you down. Some people use it to tear others down in an effort to build themselves up.
(Can you tell I live in a small town? Yeah. Gossip is like the worst part of it.)
Gossip is just part of the way of life in Quidnunc, and you ignore it to your peril. At least this is the way Alice looks at it.
Robert's opinion is that people will say what they want, and Alice should simply live her life without worrying about the gossip. Easy for him to say, since he'll just be in Quidnunc long enough to solve the mystery of The Blank Book. Then he will head back to Hollywood. But Alice knows she's stuck in Quidnunc, and she'd better do everything she can to keep her reputation intact, or she'll be stuck with the repercussions for the rest of her life. Alice struggles with the "gossip tree" throughout the book.
If you want to know the previous reasons you haven't read The Blank Book, here they are: