In the case you describe, you’re being asked to provide the names of unbiased (or relatively so) “personal references”, who will vouch for your character, honesty, attitude, etc.
Family members are obviously not unbiased, which is the reason to exclude them. Past supervisors may be focused only on your ability to perform whatever tasks were set in front of you, and while they may be unbiased, they may also not know you well, which is one of the reasons to exclude them. (There are other legal reasons for that, too, which have to do with employment law and the liability of the former employer if its employee divulges information about you. That’s probably a bigger reason for their exclusion: many employees are simply forbidden to give references to former employees of the company.)
Teachers and instructors are good references. In the first place, they can probably write decently, which cannot be gainsaid in these days of generalized illiteracy and simple carelessness with communication. In the second place, they see a lot of people that they can compare you against, so their opinion may be valuable to the prospective employer. As well, they are professionals of a sort, so their opinions may carry more value by virtue of who those people are.
If you can include neighbors, priests/ministers/rabbis and the like, that would also be helpful.
One thing that I can advise you for certain-sure is: Talk to your prospective references, first, and make sure that they are on board with this idea. Nothing can hurt your chances worse than to have a prospective employer call a reference that you have listed and have the person say either, “Who the hell is that?” or, “Boy, oh, boy, do I have some stories about that one; stories that will curl your hair!”
Contact your references first, before listing them, and get an idea at that time if their memories of you are good ones, and whether they’d be willing to be contacted. That’s a kind of professional courtesy in this area that you should always follow.