In most cases, yes, the roughness of a surface is proportional to the friction it should be capable of generating. There are exceptions; for example, extremely smooth surfaces of identical metals can actually experience such low friction that they fuse together (this is called cold welding). This phenomenon has been explained with the characterization that the atoms in the metal "don't know they're in different metals" and therefore have no reason NOT to fuse under those conditions. Cold welding isn't something you would see in everyday terms, however, and under everyday conditions you can count on rough surfaces to provide more friction.
Friction is a force between two objects that resists their perpendicular motion to each other; basically, they have to be in contact, but moving at right angles relative to each other, and friction will attempt to stop this from happening. It's the same reason why, if you have a book sitting on a table, it doesn't go scooting across the table at the slightest touch; you have to apply enough force that it "beats" the resistance of friction.
At the molecular level, most objects have imperfections in their surface texture, which basically makes them look like the teeth of a sawblade. You can think of friction as being born from these "teeth" intersecting each other, sort of like a zipper. Friction is the resistance provided by those little peaks and valleys ramming into each other and splitting up the perpendicular force into parallel and perpendicular vectors, with the perpendicular vector proportionally reducing the parallel vector and thereby resisting the object's motion.
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