What it means: When you put a single tone, say 500 Hertz, into the headphones, you should only get a single tone out. But if the headphones are "non-linear" you will get some extra energy out at other frequencies. These are called "distortion products" and happen at multiples of the fundamental test tone. In the case of a 500Hz tone, the 2nd harmonic would be at 1000Hz; the third harmonic at 1500Hz; the forth at 2000Hz, etc.
How to intrepret the line: Theoretically, the perfectly linear headphone would have no harmonic peaks whatsoever; in practice this is rarely the case. The full poindexter discussion is complex, but the general wisdom is that distortion is less audibly disturbing when the each peak gets smaller as the frequency goes up AND that the second harmonic is not nearly as disturbing as the third.
Generally, it is our experience that tight, clean, articulate-sounding headphones have few harmonic distortion products. Headphones that sound lush (thought to be the even harmonics) or hard and/or grainy (thought to be the odd harmonics) probably have a lot more harmonic distortion. It is our experience, however, that some very good-sounding headphones have a significant amount of harmonic distortion, so it would be wrong to assume that just because there are a lot of distortion products that the headphones sound poorly. It's just not the case. The ears have to be the guide here!