tl; dr: A thin, flat organism that grows around a rock.
Obviously the rock part is usually considered Earth, too, in which case I guess it would be a rock covered with a thin, flat organism.
And of course, you could say that the flat living bit is full of discrete organisms - but none of those organisms can survive outside the main "body." Not for long, and not without a special suit filled with plant breath. And unlike, say, a fetus, it doesn't look like any "discrete" organisms will develop that capability; the best we can do is reproduce the whole biome on another rock (which suggests terraforming is more analogous to reproduction of an independent organism than human space travel), or populate (infect) a very similar rock with the same kind of biome already growing on it (which would make humans analogous to viruses).
If you remove key organisms like, say, photosynthetic plants, the whole thing collapses. Even without a relatively specialized species like bees, several systems would collapse, including human civilization, which would cascade into the loss of other systems like, say, the pigeon population of St Mark's Square, or diseases like TB (?) that can only thrive in dense human populations. Which is why I think of different species as different types of cells within a larger organism.
It was popular for a while among the ecoterrorist set to compare human beings to cancer, which seemed more like a loaded political soundbyte than a realistic analogy because the thing about cancer cells is that their telomeres don't shorten, ie, they have "artificially" extended lifespans, something humans have yet to achieve. I've also seen analogies between humans and the development of a nervous system/brain, which suggests the living part of Earth is a fetal organism. Which is more interesting to me; it's not like human development is unnatural, it seems like a logical outcome of evolution that the species to use complex tools and understand how science, in particular medicine, works would thrive. It's been postulated, for example, that without the extinction event that killed off the dinosaurs, a reptilian species would have eventually gotten smart enough to fill the very same ecological niche. So maybe a "brain" species is, if not inevitable, very likely.
But then, if terraforming is the method by which the Earth organism is able to reproduce, that would make us.... well, some sort of reproductive cell? Hmmm.... but the question wasn't "what is the role of humans," so I guess that's enough of that....
"4 cylinder Camaro=communism" El Presidente
"You can smoke salmon but it's not quite the same as smoking heroin." nanuq