I understand their traditional utility is to shrink/close the pores after shaving, and to disinfect any small cuts. This is a crude way of doing both, for alcohol is not very good for the skin. It also gives a good barometer of how well you are shaving, for any microscopic injuries will sting - making you more careful. But alum is a somewhat better choice, as not alcohol-based. in modernity, anyway, I think there is no practical purpose for aftershaves. I prefer to use an unscented aftershave balm (which, on the neck, happens to give a better basis for scents to cling to).
Which leaves aftershaves' possible purpose of scent. They are a very weak concentration. I think Habit Rouge is a scent whose aftershave is occasionally admired? Personally, I don't wear them.