The husking bee was a work party. It was a way to make jobs that were potentially tedious into fun. Farm people around the world have such parties; you might have heard of a quilting bee. It's the same sort of thing.
In this case, there were special traditions or rituals. If you got a red ear of corn, you could claim a "forfeit" (a prize) of a kiss from the person of your choice. It was a party game, and a socially regulated way of letting young people get together a little bit, but not in a way that would get out of hand.
Judith got the red ear of corn, but since she thought she was already getting married, she didn't need it. She gave it to William, who came forward towards Kit to claim his forfeit. (The chapter ends there, but we can assume he kissed her.)