"Friction" means mechanical energy is wasted when two surfaces are in contact and move relative to each other. The only way to waste this energy is if both surfaces are not completely smooth, and one or both surfaces can be distorted (i.e. is not perfectly rigid). That way sound, and thus eventually heat, can be induced in the material. Obviously there's no such thing as a perfectly rigid surface--otherwise it would shatter as soon as the bumps on its surface collided with another like surface, because the collision would be instantaneous, and therefore have infinite force.
I think there are many effects that make friction non-linear, like chemical adhesion, effects of air pressure depleted in the gap, non-gaussian patterns in the roughness, and resonances.
Resonance is just the 'squeeking' one might get--like when you rub your clean fingers on clean, wet glass surface. (although your lecturer was probably thinking of much higher frequency and likewise shorter wavelengths). If there is squeeking and the friction coefficient is non-linear (pretty much all are), then the periods of strong force between the surface can have extra-strong friction compared to the friction during periods of lower force, the induced sound is stronger, and so more energy is lost.