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, sevennight and sen-night, as in a letter written by Edward Gibbon in April 1777: “The day of my departure is not absolutely fixed; Sunday sen-night, the 27th instant, is talked of: but if any India business should come on after the Civil list, it will occasion some delay.”
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 from everyday life by competition with the shorter week.
It has had some continuing existence as a deliberate archaism, especially in historical and fantasy novels:
The tailor, she found after breakfast, was away on a trip. “Buying cloth up at the Count’s fair,” said his wife. “He’s got a commission to make cloaks for the new council members, and has gone to buy cloth. He won’t be home for a sennight or more.”
The Deed of Paksenarrion, by Elizabeth Moon, 1992.