well, going to a different business, and executive, does have an executive assistant, one that answers phones, makes appointment, etc.
So lets look at what a captain's yeoman could do? Well lets see.
Serve as a go between, captain is.. captaining.. so people contact him/her/slithern to scheduale a meeting, or other things. done by computer? possible.
Its basically a command paper pusher/clerk
paperwork for promotions, transfers, etc.
Monitor, keep records for consumables (Fuel, food, etc.) what Kirk signs on most episodes, fuel consumption reports etc.
In charge of supplys, whom you request your stuff from.
Writter of speeches, prepare reports, person of knowledge on protocols, honors, ceremonies, maybe for visiting vips prepare reports on culture, etc. for the captain to read before a meeting. up to date on whatever planet there visiting.
Sort fitness reports.
So basically, someone who helps with all the paper/mundane stuff on a ship.