Fidgeting is a derogatory term for not holding one's body still, especially while sitting, e.g. during meals, in church, or at school. Fidgeting is often a sign of boredom or lack of self-control, or interpreted as such.
Traditionally, children are expected to sit still at these occasions so they won't disturb other people present. Often, they find it difficult to do so, and so have to be reminded not to fidget, and reproved (with words such as "stop fidgeting") or punished if they can't keep from fidgeting. The latter is a typical Victorian era and Edwardian era scenario, but is also found before and after those eras, up to present day.
An example of punishment for fidgeting in a spanking novel is chapter 5 of The Old Rectory, where Alernon Briggs, a snotty ten-year-old boy and non-boarder, is reproved and punished (by having his legs slapped a few times) for fidgeting at the lunch table, after Henry and Eddie had secretly put some itching powder in his stockings.
Unterbrochene Mahlzeit (Disrupted meal), painting by Heinrich Franz Gaudenz von Rustige (1838)