Not a silly question at all.
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CookieMonster said, it'll develop more flavor overnight (or up to three days), going through a slower fermentation process. It'll also improve the the texture/chew of the crust. You know that "baker's window" everyone wants in the pizza dough, where you can stretch the dough so thin without tearing that you can see through it? That's hard to get with a short rise, but easy with an overnight rise.
Most decent pizza places overnight their dough, though they also have a backup same-day recipe (usually referred to as "emergency dough") in case something catastrophic happens with the overnight dough.
Same-day and overnight doughs vary a bit in their prep, mainly in the amount of yeast. You'll use a lot more for a same-day dough. Overnight dough...I use a scant 1/4 tsp of yeast. You don't need as much, because it has all night to get its work done.
If you make the same-day dough, and then compare it to an overnight dough, I'd wager you'll pick up on the differences pretty quickly. The same-day dough has a tighter crumb, less flavor, less pull/chew. The overnight dough will be more pillowy, more airy, and have a really nice toughness to it. Tough, but in a good way. And the flavor is much better. I rarely make a same-day dough and remark on the taste of the crust. It's there to hold up the toppings and to otherwise stay out of the way. The overnight dough? I'll have a tough time deciding which end to start first, because the crust with nothing on it tastes so good.
I'll dig around and see if I can find some pics of overnight dough that I've done. They don't even look the same.