In short - to make it sound fuller and more harmonic. As stitch said thats how guitar and standard tuning are laid out, so why not take advantage of it and play something more than just 3 notes on 3 strings? 
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Justin states in the video (about 2 mins 20)
‘the more discoveries you make on your own the better’.
There are only five possible open position chord shapes for major chords - C, A, G, E, D.
You know that a triad must contain the 1, 3 and 5 (for minor 1, b3 and 5).
Use your knowledge of chord shapes, notes in the first three frets, triad construction etc. to find all possible triads on adjacent strings in all five of these shapes. Repeat for Am, Dm and Em chords.
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it may be that this question has been already asked and addressed somewhere else, I give it a try: are triads as defined in this module always to be found on consecutive strings? 1-2-3, 2-3-4, 3-4-5, 4-5-6 ?
Memorising the possibilities with the classical C-A-G-E-D shapes, one can transfer the triads along the neck to any key, an easy way to memorise notes on the neck and also visualise triads.
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They are often the easiest to play on adjacent strings, but they don’t necessarily have to be. If you play, say, x32xx3 (on strings 1-4-5), it will still be a C major triad.
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OK, thanks József, that opens up even more possibilities. The magics of guitar compared to a piano. How I love this instrument (the guitar, hence).
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Yep. Called closed triads on adjacent strings.
The other type is open or spread triads, that span greater distances, usually greater than an octave.
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THX Shane, good to know
I have mentioned closed and open tridas previously
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Thanks Richard, as mentioned to József, having triads on conjoint strings as well as open triads open up quite a huge territory of tone for the same chord.
So let our ears define what shall be the right one in the melodic context. The rest will be a question of musical taste.
by the way, creating chord schemes of all the triads, starting from open chords shed quite much light on where to find them. Last but not least, triads on strings 4-5-6 appears to be identical as for strings 3-4-5. Wonder why? And what about the augmented shapes, the next discovery.
And this is the magic of the guitar !
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Guitars are tuned in 4ths except for the B string. This is why the grips are the same except when the B string is involved.
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actually these are the missing links on strings 4-5-6