What do different Cepstral or MFCC coefficients represent intuitively?
When you take the log of some measurement value, you are simply changing the nature of the scale of what you are measuring.  Where the dividing line between positive and negative values on the new scale is depends only where the &quot;1&quot; was defined on the original scale.  There is no qualitative distinction between positive and negative per se, so what you are really asking is why are slowly changing components (lower coefficients) larger than other ones.
If a sinusoidal is enlarged proportionally, then the amplitude is inversely proportional to the frequency.  If your signal indicates this (regardless of context) it means similarity is being preserved across levels.
So this doesn't answer the title question, but hopefully helps with the enclosed ones.