Viewing things at the atomic level, it is electrical force between each atom's outermost electrons that keep an object in one piece; because the atoms of the object share electrons. When two objects come together, the repulsive electrical forces between their outermost atoms keep the objects apart. This means that each object's outermost atoms get pushed in towards the layer inside them, moving those atoms too. These movements spread through the object: and when atoms in an object make small movements without actually swapping places with each other, we call that heat. The ordered motion energy of the two objects "disappears" - because it just got turned into disordered motion energy of their internal atoms. Both at the atomic level and on larger scales, the electric field summed up from all the outermost electrons is bumpy, not smooth (even highly polished surfaces are not atomically smooth, perhaps some monocrystalline structures are). So when you press two objects together and slide them across each other, they're continually riding up across each other's bumps and sliding into each other's dips. For every bump, mechanical energy is lost and turned into internal heat energy. So the force you apply to get the bumps to ride up isn't completely paid for by the slide downhill on the other side. You feel this as a frictional force opposing the movement you're trying to make. It's always exactly proportional to the force pressing the objects together, but it's also affected by how fast you push. That's what makes the difference between static friction and moving friction. Like when you're trying to push a car along a bumpy track. Even if it's in neutral, you lose energy each time it rolls into the next pothole.
