Aaah yes, older men. One of the few guy types in otome games I tend to be all over.
But what makes someone like that attractive? Forgive me for any bouts of fangirling that may occur, but I will try to explain it by giving an example.
(Yes, I'm a nerd and have thought WAY too much about this character. Shut up.)
This character has a LOT of fangirls, much more than you would think. At first glance, it might be hard to understand why. He's neither nice, nor attractive, nor particularly rich. And still fangirls are all over him. Not to mention that one of the most popular 'romance options' in fanfiction for him is Hermione Granger. A girl who is about 15 to 20 years younger than him. And this fandom has some of the best and most in-character fanfics I've ever read.
I will use him and this pairing as an example, because it's perfect to show an attraction that is not based on looks and pretty much lives on the smaller, more subtle things.
Severus is nothing if not mature. Unlike characters like Ron, he does not care for childish behaviour and is very down to earth. (*coughdunderheadscough*) This also implies a sense of responsibility that (if you look at it from the cavewoman perspective) signals the ability to care and provide for a female/family. Since girls also mature faster mentally than boys, it is not unreasonable to think that one such girl might feel an attraction towards this maturity. (In the particular case of Snape/Hermione, my shipper heart might also like to add that Hermione should not have to put up with someone who doesn't value her intellect. Which reminds me of...)
Also the reason why teachers in otome games are so very attractive. Intelligence is HOT. End of discussion. No one can deny that Snape is one of the most intelligent characters in that book and it gives him an air of sophistication, which is attractive to a lot of girls.
No matter if you see it from a general or a sexual perspective, older men have more experience. They have lived longer and experienced more than the average young man. They have been shaped by their past and have the scars to prove it. No matter if their life was hard or easy, loving or full of rejection and pain, their personality is full of layers showing what they've been through. Again, Snape is a prime example. He lost his childhood friend and love because of his own stubbornness, to his tormentor no less, made the biggest mistake of his life by joining the Death Eaters (for which he suffers until the very day he dies), was unable to protect his childhood love from death, changed back to the good side, is always in danger of being killed for being a double spy, is forced to protect the child of his bully (who, by the way, continuedly accuses him of working for the wrong side and makes his life generally harder), is hated by almost everyone and no matter what he does, he never gets one word of thanks. So yeah, his experiences and past made him the man he is. And you can't tell me such a character is less interesting than the 17 year old popular basketball player who never once left his home town. And when it comes to sad pasts, well, isn't it nice to imagine being the one to coax the broken, hurting man out of his shell?
Especially in fantasy works, this is an important point. The older character will always be more powerful than the younger ones (unless the younger character has some sort of super-mega-foxy-awesome Mary Sue powers) and is therefore a better protector. Again, Cavewoman is satisfied when she knows she and her children are in safe hands.
This is the result of all of the above mentioned points. It all adds up to this. Charisma. No matter if the character is outwardly hot or not, no matter if he's grumpy or not, he will always have a special sort of charisma that draws girls to him.
Snape is a grumpy, humourless, rather unattractive man. But he has charisma. And it makes him hot. (The fact that he is a deadpan snarker also helps.)
Obviously, all of this does not only apply to Snape, but older men in general.
I might have talked a bit too much about him and I apologize, but everytime 'older men' and 'attraction' are mentioned in the same sentence, I just can't help myself. I'm a terrible fangirl.
EDIT: Now I almost forgot the point that may or may not be the most important one:
6. Forbidden love is best love
Because what could be more exciting than the forbidden love between a 17 year old girl and a much older guy, who may also be her teacher on top of that? I don't know if it can be called romantic, but there's just something about a guy risking jail because he can't help but love someone. xD