As people have stated above the purpose of aftershave (alchohol) is to disinfect the skin and close the pores. Some also find it has a cooling or bracing effect. If you suffer from razor burn or rash then it can serve as an analgesic, but it's also likely to sting for some time first depending on how oily or dry your skin is. On the negative side alchohol can potentially dry out the skin, and some even say it can cause it to become scaly or tough. The bottom line though is millions of men used these products everyday for most of their lives and did not find them wanting. There's no reason to avoid it because it's old. It gets the job done. Of course if you prefer a balm of some sort that's effective as well and probably less painful. You really need to work out your own routine when it comes to these things. Something that suits you.
As far as fragrance is concerned others have covered this. An aftershave will be weaker than the corresponding EDT or Cologne, but that doesn't mean it's useless. Some EDTs are incredibly strong, even prohibitively so, which means the corresponding aftershave might actually have servicable longevity and projection. I own a few 220ml bottles of vintage Givenchy Gentleman aftershave for example and they are as strong and long-lasting as most of my modern EDTs. Though not as strong, or long-lasting as the vintage EDT itself. The scent is also a little deeper in the EDT which makes the aftershave more wearable in certain situations. Simmilarly the Obsession, Coriolan and Joop! Homme aftershaves are all viable fragrances. There are others I've come across, but I won't go into detail listing them all.
I use aftershave after shaving on occasion. It depends entirely upon my mood. Other times I use a splash of cold water followed by a post-shave balm. Sometimes I want to feel that stinging sensation and get a nice whiff of scent, but generally speaking I don't buy aftershaves for all my fragrances, and the ones I enjoy as fragrance are not for splashing on willy-nilly. For me the ideal aftershave is something with a limited longevity so I can splash it on and enjoy it, but not have it last too long and interfere with my fragrance of the day. It's something I might use on a lazy Sunday morning, or when on holiday when I have the luxury of time. I don't want it to last beyond midday.
That said generally I use EDC's instead of actual 'aftershave,' because the alchohol content is not that important (above 60% there is little difference in reducing bacteria count, and that's only relevant if you cut yourself and I use a stypic pencil on cuts which disinfects anyway) which at the moment means either CDG's Citrico, Vetiveru or Anbar, Eau du Coq, English Leather, Roger & Gallet's Vetiver or one of a few cheapy colognes by Mont St. Michel: Ambree, Rose, or Naturelle (Bergamot) which I like because they only last for about a half-hour, and they smell nice.