Example:
Most (but not all) of the gameworld consists of about 100 fairly generic settlements - some of them rural, others mining towns, ports, whatever fits - spread across a varied, vast expanse of similarly generic plains, swamps, hills, forests, ravines and mountains.
Your quest: "Defend against an incoming invasion." You took this quest and you'll try to achieve this goal.
That's it. There are no sub-goals stated for you, you're in charge of creating them yourself. There is no one true way to accomplish it, you have to be creative. There is no guarantee of success, and the most likely outcome is less than absolute - both absolute victory and absolute defeat should be fairly unlikely.
Let's assume you decide to try and raise an army, so you gather support from the settlements, buy or threaten them into your service where they aren't willing, decide on which people to train what and appoint captains for your army. You don't
have to do it, of course, you could as well try diplomatic approaches, or try to penetrate the enemy's defences and kill their leaders, or a dozen more stuff nobody specially programmed in or predicted. But let's assume for a moment you decided to do it the fighter's way.
As you sit in your tent watching the map, the information comes in: The main enemy army has been spotted moving along a narrow ravine to one of the generic settlements. You were there before, it's a dozen homes to as many families, by the name of "Isaernwater". There is a good place to stop them nearby, so you decide to gather your troops and order them to move there, to your designated battlefield. A few days later, you manage to stop the other army. There is a big fight, hundredths die or are maimed for life, but your final charge manages to reach the enemy's encampment, break through and take their leaders prisoner. Your quest is fulfilled, even though a part of the country fell into the invader's arms. Sadly, in the midst of the fighting some of enemy's troops fall back to Isaernwater, and most of the place burns down, with a good portion of the population dying or fleeing into the woods, never to be seen again.
Two years later, you happen upon that place again. Most of the burned-down husks of the old building are overgrown by ivy, young birches grow in the ruins. A few houses have been rebuild though, and the inhabitants greet the hero of the war with great joy. There is a two year old girl here too, a sweet little child with curly blonde hair and big brown eyes. They tell you she's been born on the day of the battle, and her mother perished shortly after, so they took her and raised her as their own daughter. They called her "Victoria", to commemorate your victory.
In a game with a good, extensive game system, all of this would happen without
any of this being scripted. Next time you play, you might decide to tackle the invasion another way, or the invading army would try a different approach, and none of this would happen - but other stuff would. Victoria might not even be born at all. Or maybe she would, but without a big battle nearby happening at the right moment, she'd be called "Saretis" after her grandmother instead.
That is how I want a sandbox RPG to work. I don't mind a generic background, I will change it and create my own through my play.