The best example is character generation. Rolling random stats - in order - gives you something to work with. You're smart rather than quick or strong or persuasive or observant - if you can find a Wizard to teach you, you may have a bright future. You're big and strong, pick up a sword and you might go far.
To really take it all the way, you'd want to start with randomly determining race (weighted by the various populations, or better yet, birth rates of the various races), then culture (based on the distribution of that race among the campaign's cultures), then social class, and, only then, with modifiers for race, culture, and social class, would you roll some stats. If you're a noble-born human you might be more likely to have good STR & CON, because you have a goo diet - and if your ambition is to become a knight (and you were randomly born male), you're likely to realize it. OTOH, if the third noble son of a house traditionally goes into the clergy (and that's your random birth order), off you go to Cleric school.
A DM could go into great detail coming up with tables to determine all that sort of thing - especially if he's a bored 15 year old on his second summer vacation after discovering D&D...
*ahem*
...I have said too much...