BBB Etymology - Yeoman's Duty
The Yeoman of the Guard refers to the foreman or, in today's terms, a NCO (non-commisioned officer) or Petty Officer, i.e. only slightly elevated above the people he commands. Foot soldiers were a notoriously unreliable and lazy lot, often pressed into service against their will. The Yeoman would have been one of their own who proved especially trustworthy and who commanded the obedience of those beneath him.
Hence, the "Yeoman's Duty" was an assignment given to the Yeoman to be carried out by him alone, and not entrusted to the rank and file. This task may be something that might ordinarily be given to a common soldier (not difficult or arduous) but for the importance of it being carried out with attention and in a timely fashion. Serving Yeoman's Duty is to faithfully carry out whatever task is given, even the menial.
Hence, the "Yeoman's Duty" was an assignment given to the Yeoman to be carried out by him alone, and not entrusted to the rank and file. This task may be something that might ordinarily be given to a common soldier (not difficult or arduous) but for the importance of it being carried out with attention and in a timely fashion. Serving Yeoman's Duty is to faithfully carry out whatever task is given, even the menial.