AbdulAlhazred
Legend
What he's trying to describe is a situation in which various character traits, backstory, goals, bonds, etc. feature fairly heavily in how the action is directed. So when one would ask "why did the the party travel to Mudberg?" the answer is "Because Joe got a message from his sister telling him she's worried that her son is in trouble with some local thugs." or something like that. Note that the player may have established the existence of the sister as part of backstory, perhaps even the nephew. Other than that, the 'hook' was probably built by the GM, and pulls the PCs into some sort of plot or perhaps just a straight up standard adventure scenario with the hook added. Later, during the adventure, the hook may come up again and present the character with some sort of motivation (IE the nephew is held hostage by the bad guys with the obvious implication that the PCs better go away or else). Various dilemmas may be posed, and these may well speak to elements of the character (do I leave the bad guys alone to prey on the town and save my relative?) etc. Treasure and glory will generally also be there as sort of baseline table stakes. The PCs will usually accumulate some roster of enemies, etc.That's not quite sufficient for character driven. Character driven is where the game centers on the characters. If the characters are motivated, say, to plunder a dungeon and gain treasure, this isn't character driven because the play is actually centered around the setting -- exploring the dungeon created by the GM for the setting (or provided in a module). The characters are motivated to explore the setting. This is great -- it described my 5e games pretty well. Along the way, we can get character moments, but the organizing feature of play isn't the characters, it's still the setting.
For it to be character driven play, play has to organize around the characters, such that setting is introduce only as backdrop and as needed due to what the characters are about.
It's a rather large distinction in play. Doesn't sound large here, but the impact and effect is night and day noticeable (not that one is night and the other day).
Obviously you and I see a really significant difference between the above and what something like Dungeon World is doing, where setting only exists to the extent that it literally comes into play (the GM may plan for more, but nothing which hasn't appeared in play is canonical in any sense). Players are COMPLETELY in charge of all the areas which relate to their characters directly, and the story is built directly from that.
It can be hard to parse, I guess, because you could certainly POTENTIALLY generate some pretty similar narratives. At least you could look at a DW session and imagine that much of it is not violently at variance with things that could be depicted in a 5e game. I can only suggest that @clearstream and @Crimson Longinus might try playing some PbtAs under an experienced GM like yourself or @Manbearcat in order to really see how different the process of play really is.