They are apparently trying to show more diversity within the Klingon people (do all earthlings look exactly the same, have the same clothing choices, etc...) - in other words, moving away from a planetwide monoculture (or, retconning that we have until now, only seen one or two houses)
Discovery indicated in Ep1/2 that there are 24 Great Houses. These two episodes showed one of the houses which seems to have distinct design and biological diversity from what Klingons have been shown in previous series.
Here is some behind the scenes detail:
Mitchell explained we have only seen some of the Klingons from
The images that you have seen so far are one house led by T’Kumva.
Today you just saw the first image of [Kol]. So even in the wardrobe
it is starting to venture to the more traditional Klingons. More
leather and a different set of armor. And the series itself is going
to explore 24 different houses and the leaders among them. And you
will find different complexities and different ideologies amongst
those houses. And so what you have seen already in these images is
mostly just from one house. You are going to start to explore further
into the Klingons, and each of those houses has a different set of
physical looks and variations as well as ideologies.
Here are some additional details on the early redesign from Bryan Fuller:
The other Bryan Fuller contribution that remains is his redesign of
the Klingons. “One of the things he really, really wanted to do was
shake up the design of the Klingons,” Herberts said. “One of the first
things that he ever pitched to us when we were deciding whether or not
to come on the show was his aesthetic for the Klingons and how
important it was that they be aesthete, that they not be the thugs of
the universe, that they be sexy and vital and different from what had