In quick "layman's terms", assuming from your question that you are not familiar with harmonics:
Harmonics are caused by the non-linear way power is extracted by a rectifier from an AC system. It's not really pulling power out continuously from the sine wave, but rather in "gulps" near the peaks. This causes a distortion of the incoming line power sine wave. The shape of the distortion can be analyzed and broken down into a series of "harmonics" which can be thought of as superimposed frequencies existing on top of the fundamental frequency of 60 (or 50) Hz, referred to as multiples of the fundamental. So a harmonic frequency of 120Hz would be a "2nd" harmonic, because it is at 2X the fundamental, a 3rd would be 180Hz, a 5th, 300hz etc. etc. In a 3 phase system, harmonic frequencies on individual phases that are "opposite" each other in each phase will either cancel each other out or add together. Even "order" harmonics, i.e. 2nd, 4th, 6th etc. will cancel each other out. Odd orders that are multiples of 3 will add together in the neutral of a transformer and that is bad (I'll forgo further details on this for this discussion). "Non-triplen odd order harmonics", i.e. 5th, 7th, 11th etc. are also additive but represent a less significant problem for power distribution equipment.
By using multiple rectifiers and feeding them with phase shifting transformers, you "rotate" these odd-order triplen harmonics with relation to each other by the induced phase shift, i.e. 30deg, 60deg, etc. etc. So the more you can shift, the more they become either even numbers with relation to each other, or non-triplen and therefore not as destructive. taht video shows the net effect as they increase the number of phase shifts; the more the merrier!
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