To shake one's head (usually left-right) to indicate refusal, disagreement, or negation.
彼女はその申し出に対して首を振って断った。
She shook her head and declined the offer.
会議でその案には多くの人が首を振った。
Many people shook their heads at that proposal during the meeting.
医者は首を振りながら『原因ははっきりしません』と言った。
The doctor shook his head and said, 'The cause is unclear.'