Pull a tensioned string, and it will start making wave movements. Funny thing is, there are big waves and smaller ones at the same time. Big waves make fundamental notes, small ones overtones. Pinching harmonics, or playing flageolets (flute tones) if you're into fancy musical words, is deadening larger size waves (usually only one or two) and leaving the others to continue. The result is you only hear the overtones.
Why doesn't it work well on a ukulele? Well, because if you only let the smaller waves continue, then the sound will become very thin indeed on a short scale: there's simply very little string movement anymore. 12th fret harmonics and 5th fret ones are okay, 7th or 3rd are hard/impossible to get right. Same with fretted harmonics, which require precise dampening and a challenge on a ukulele.
Longer strings make those smaller waves still audible, and steel strings more so then nylons, although good classical guitarists can play impressive flageleots.
One way around is to use larger scale ukuleles, and use electrical amplification. Oh, and practice!