Same as it does on a rough surface.
You get the oils polymerizing, which is going to stick to pretty much anything, no matter how smooth it looks. The surface isn’t microscopically smooth, there’s still roughness.
However, it wouldn’t matter if it was perfectly smooth. The bonding between the iron and the oils isn’t purely mechanical. It bonds on a molecular level, meaning that the little bits on the atoms of the polymerized oil make sweet, slippery love to the little bits on the atoms of the pan.
A smoother surface is actually better. You don’t have as irregular a surface on the polymer, and there’s less gaps where they contact the metal. Which, ideally, you’ll be applying very thin coats and prevent gaps, but it’s never a perfect process.
Sanding down a pan before seasoning improves the bond, improves the cooking surface, and makes it easier to season.
You ever use a stainless steel pan of some kind and have oil get solid-ish on it? It leaves that layer of brownish, maybe amber stuff that’s slick and hard to scrape off. It’s the same thing. You can polish stainless still to a mirror finish and that will still happen, and it’ll still be difficult to remove.
When it comes to that, a rough surface is more likely to chip, flake, or otherwise fail.
Your best seasoned pan is going to be sanded smooth, then seasoned with food grade flax oil (though it is by no means the only option, it’s the best drying oil that’s food grade). You’ll cycle it three to five times, depending on your freedom to do so. Then you’ll have very low stick, heat resistant surface.
Now, nothing is perfect. If you can’t get flaxseed, stuff like canola that’s semi hardening will work almost as well (most of the time, you can’t tell the difference until or unless you abuse the hell out of the pan). If you can’t get that, any oil that’s safe to eat will get the job done to some degree, so long as it’s heat reactive at oven temps. Which, if you can’t get flaxseed, the chances of being able to source anything that unusual isn’t likely to begin with.
I dunno for sure, but that looks like something in the 400 grit range followed by steel wool.
It’s a lot of work tbh. Enough so that I don’t do it any more.
But, it does improve the cooking surface. You sand down and season with flax oil, and you’ve got a great surface that even eggs won’t give you too much trouble cleaning up.
It doesn’t have to be perfectly smooth, mirror finish. And some small pits are okay. No need to really grind the hell out of a pan, you just want to kinda even it out so there’s less texture, with the end point being where you decide is good enough.
Back the last time I did one, I used an orbital sander with 200/400/600 progression, then hand sanded to 800, and it was more than smooth enough. Going past that is diminishing returns. I’ve seen people do a mirror finish and it wasn’t worth the time imo. Even 800 is kinda extra tbh. You just don’t want highly visible scratches.