If your mother only remembers the good things and not the bad, she has a selective memory. If a school chooses to offer only a few students spots, it is selective. Selective means characterized by choice.
When you are looking for someone to date, you will get advice as to how selective to be. Some people will suggest that you cast a wide net, choosing to date a lot of people in hopes that one will be right. Others will recommend that you be more selective, choosing to date only people that fit a set of criteria. If you are a male, you will have to register with Selective Service, a database the military selects from if there is ever a draft, when you turn 18.