An allowance made to the master or owners of a ship by the freighters for detaining her in port longer than the time agreed upon. (Latin, demorari, to delay.)
“The extra days beyond the lay days ... are called days of demurrage.” —Kent: Commentaries, vol. iii. part v. lecture xlvii. p. 159.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Demurrage from Fact Monster: