Cleans your hair ...
It comes from an age when men didn't ... well, wash often. Weekly bath. Hair washing with shampoo was probably something that dandies did, but most fellows didn't. In fact, many fellows (certainly up my way) would not wear a wedding ring because chaps did not wear jewellry and certainly did not wear EDT - aftershave (at best) was a thing for young fellows.
It's from an age when men lavished greasy pomades on their heads, before hipsters with their beards were reviving it as a "grooming" thing. It's from an age when a chap would pop to the Barber's, thumb through some well thumbed mens' magazines, have a hair cut and the Barber would pat a drop of hair tonic on.
I'm a traditional fellow. I do wash regularly, but rarely shampoo. I use a dot of Brylcreem on towel dried hair in the morning and then a damn good splash of hair tonic after my evening wash and shave. It keeps the hair clean.