Among Germanic peoples it was once normal to record the passage of time by the number of nights rather than days. Sennight is an abbreviation of the fuller phrase seven nights, hence a week. So Sir Thomas Malory wrote in Le Mort d’Arthur (1485): “They sojourned there a sennight, and were well eased of their wounds, and at the last departed”.
It has been written in various ways down the centuries, for example as sen’night and sevennight. The same process led to fortnight from fourteen nights.
It’s a quirk of the language that fortnight has survived as standard British English (though not American) while sennight is now defunct. It did last into the twentieth century in some areas as a dialect term, though eventually driven out by competition with the shorter week.