If you're impersonal, you're neutral — you're not showing your feelings or your preference. If you choose people to be on your team by closing your eyes and pointing, that's impersonal — you're not picking your friends or the best players.
Impersonal can be good. An impersonal rejection is easier to take than one that specifies precisely why you, in particular, are a reject. But if your class is so impersonal, your teacher doesn't even know your name, that’s not good. A wedding that doesn't include details about the bride and groom would be impersonal and maybe more like a business meeting than a celebration. Impersonal comes from the Latin roots in- (or im-), "not," and personalis, "of a person."