It effects how a few of the quests can play out.
For example the first mission where you have to go to the pub and get info from the private detective guy, if you are smart enough you can just threaten him for the info and it will end there or if you do one of the other options he can ask you for help to get evidence that the man he is watching is cheating on his wife if you are smart enough you can get both the info you need and money he offers you in advance and just leave.
It also can have an effect on different repeatable events like having sex with bar patrons when you ask them to do anal if you are smart enough you can convince them to this can be helpful if you don't want to risk getting pregnant.
If you don't already know you can increase your education by going to class (duh) and studying in the library on the second floor.