Tribrachidium is from that oddest of time periods, the Ediacaran, and because of that we can partly excuse it for its weirdness. It's basically an Isle of Man flag with frilly bits at the edges:
Tribrachidium is a member of a very exclusive club of organisms: those which have a body plan based on 3-fold rotational symmetry. This is completely unique; even echinoderms (starfishes etc) are really bilaterally symmetric at heart; the five fold symmetry is superimposed on this symmetry in adulthood. Whereas, for tribrachidium, its triradial symmetry is the only sort it has. Trilobozoa is such an elite club that all the members of it that we know of could fit in a shoebox with room to spare - and they're not even that tiny. And, yes, they are all only found in the Ediacaran.
All of phylum Trilobozoa
You may not think that's not particularly intriguing; after all, there are many families that exist on the basis of only one type species. But, think about it: three-fold radial symmetry is an entirely different way of building bodies. A gaping chasm of evolutionary morphospace lies between us bilaterians (me, you, stick insects, snails, T. rexes) and these trilaterians. Our common ancestor with Tribrachidium clearly lies very deep back in ancient Earth time.
And, perhaps more incredible, is that this is a body plan that failed. We can't go fishing in some rock pool and pull out an ugly creature that is descended from this group. Nor can we find any of their decendents in rocks from the past 500 million years or so. Nature's experiment with three fold symmetry just didn't make it as far as the Cambrian Explosion.
As for why, though, who can tell? Tribrachidium is like all its contemporaries in being exclusively associated with the Ediacaran period and the strange algal-death mask style of preservation. Our ancestors were out there in those Ediacaran seas somewhere, but they have not left any trace in the fossil record that we have found. All that is apparent from the Ediacaran fauna is that at the end, there was the equivalent of an Etch-a-Sketch shake-clean of all these wonderful animals (if we can even call them animals). We may have lost the ability to preserve them for a long time that we cannot see, but whatever the extent of this, Tribrachidium went extinct.
Who was the last Tribrachidium alive? It's funny, because however unremarkable the sorry little beastie was, and however unremarkable its sorry little death was, with its death went an entire foray into a body architecture that has never been tried again. I always wonder, what if it had made it? What if we had a time machine, and we went back and protected and bred the things - like a kind of inverse Sound of Thunder? Would the world today be inhabited with weird intelligent being with triradial symmetry?
Oh, if only we could actually do such a thing! That would be a hoot, I can tell you.