You will find this expression in older writing. It's not much used any more. It means that the whiskey glass is filled to the height of a finger held horizontally, that is, parallel to the table on which the whiskey glass sits.
I'll look around for the etymology. For now, just assume it's about one half inch of liquid in a glass.
I did not find the origin of the term, but there is this:
As a unit of measure (M.E.) it represents the breadth of a finger, about three-quarters of an inch.