Generally, harmonics mean the overtones associated with sounds. For example, if I strike an "a" key on the piano and the string is tuned to vibrate at 440 cycles per second, the sound that predominantly comes out of the piano will be "a" at 440. However, the piano string itself will give off other sound waves in addition to those at 440 cycles per second. For example it may give off additional waves at 880 (one octave above) and 1300 and 1720 and more. These are harmonic overtones and most instruments project them along with the predominant sound of each note.
Additionally, when I strike the "a" key, the piano box itself and the other strings in the piano will vibrate to some extent from the energy released when striking the "a". These extra sounds give all instruments unique character. My explanation is imprecise and any physicist is welcome to chime in here.
When harmonics and these extra sympathetic tones cannot be heard, most instruments will sound boring. When they cannot be heard or they are squashed, I call it "veiled". One can have a system that while it projects the "a" at 440 very cleanly, it sounds "dry" or lifeless, because the harmonics and other extra (ambient) sounds are missing.
In my experience, tube gear does best at reproducing harmonics and ambient sounds and the less feedback used, the better. At this stage in my hobby, I'm unlikely to consider any amp with more than about 1 to 2 db of negative feedback (and zero is preferred) and I have never heard a solid state amp that really pleased me (not saying it does not exist).
So, what do "veiled" harmonics sound like? Well, put the lid down on the piano, throw some heavy blankets on top and you get the idea. You will still hear the "a", but a lot of its overtones and the piano's ambient sounds will be damped or killed. Or, compare the sound of an electric fender rhodes piano to a real piano, hence the reason for the wane in popularity of the fender piano.
