Why is friction more intense on rough surfaces?
"Rough" is a qualitative term, meaning it describes human experience rather than the explanations for that experience. In more precise terms, something that is "rough" has an uneven surface; we can think of rough objects, if viewed through a microscope, as having many jagged bumps and dips in their surface, as opposed to a perfectly smooth object, which would be completely flat at the molecular level.
Friction comes from the interaction of objects with one another at tangential angles to their motion; in this case, we must acknowledge that our own bodies are relatively "rough" as well. Consider your fingerprints, which are essentially bumps and dips in the surface texture of your skin. When you touch a similar object, friction isn't very relevant at first, because you're not moving at tangential angles to one another. However, if you try to drag your finger across the surface, you'll feel friction. This is because all the bumps and dips in the two surfaces are interacting with each other, and are pushing against one another as you move, sort of in the same way that your teeth interlock when you close your mouth, but you feel them pressing against each other if you try to move your jaw left or right.
Rough objects simply have more and/or more extreme irregularities in their surfaces, which increase the amount of tangential force experienced when you try to move against them. There are, of course, exceptions to this, because friction is the result of a variety of forces rather than just surface texture exclusively.