So, you start with the single Eukaryotic cell, just your average flaggets running around eating and reproducing. Just like the first animals, they were individuals doing their own thing, coming together to exchange information sometimes for sexual reproduction but mostly on their own. Some of these cells, through evolution, found it beneficial to move together when certain chemicals were released by other cells of the same type. Amoeba's do this when stressed (They form slugs kind of) and choanoflagellate, probably animals common ancestor, do this as well. It's a really simple form of communication, chemical goes out, others come, their nucleas contained information which attracted them to the simple messages. You can compare this to the start of human complex communication (Really, a bunch of animals can do this, but its just a rough analogy--essentially though, humanity before language but still able to work and communicate in a group).
Somewhere along the line, those colonies of cells learned how to detect chemicals (Communication) from other types of colonies, who were beneficial to be around (One possible explanation for multi-cellular life, plants, animals ect). Over time the information exchanges became more sophisticated, to the point where what could be communicated was specialized and and far more specific (IE a chemical released which only stimulates one type of cell in the large system), which lead to specialized tissues and organs made up of specific cells being selected for, including rudimentary specialized cells for conveyance of the genetic structure of all the different specialized cells in the organism (Specialized sexual cells--which means each generation could continue to use natural selection to specialize individual cell types further thanks to that communication system selecting for them). The analogy in humans is fully developed language. It allowed us to convey far more sophisticated and specialized information, passing on techniques, and knowledge, which allowed us to begin working with and changing other species, just as the multicelluars slowly specialized their various tissues with better communication, we continually specialized our tools, our dominance of plants (Farming) and other animals (Livestock, dogs ect). (Technically you could make the case symbiotic organisms already existed which specialized to animals, like gut bacteria, but again, rough analogy).
Eventually advanced animals and plants had sophisticated chemical communication systems internally, with specialized chemicals, and cells, and pathways, for fairly complex communication to more and more specialized subdivisions (Just continued specialization and advancement, but of the same basic system, transferring chemicals). This would be analogous to human writing. The ability to carry the verbal language in unique ways, long distances (And store it more accurately). Things like roads, and our domination of other animals, and plants, all help with this. The next big segregating factor for multi-cellular was was the nervous system, allowing much faster, much more accurate information transfer between cell groups (Organs, tissues). Simple invertebrate don't have brains (Jellyfish, Starfish, Hydras ect), but do have these, letting stimulation instantly cause a specific reaction elsewhere (but heavily restricted to simple messages). The human analogy would be the telegraph. Far more information, far more accurately, and specifically, far faster than writing could convey (But heavily restricted to narrower message types). Then certain animals developed ganglia, processing structures which allowed hubs to distribute and receive information, which allowed far more complex and nuanced information (Allowing more sensory information and better distribution to more cell subdivisions). The human analogy would be the telephone and the television/radio, with a far higher volume of information transferred, and far more distribution throughout to individual humans, and more importantly, a much higher complexity of information. So more people could receive and send information.
Eventually animals grew more and more complex nervous systems and brains (I'm not saying it was a single path, but some were selected that way). The brain allows for extremely efficient processing of both information received, and distributed, with many ganglia throughout the organism--allowing enormous complexity in ideas, and far more multilateral movement of information. The human analogy would be computers and the internet, multilateral information with powerful processing nodes, like ganglia, everywhere and growing centralized information transfers (Servers). Eventually, humans, like the cells which became specialized around the nervous system, integrate and specialize far more until the organism works together at a level that's the functional difference between a starfish (Humans circa 1800's), and a lobster (Humans circa 1950's), and a large complex animal like an eagle or rodent (Humans circa today). Eventually as we integrate more fully with our nervous system, and our communication becomes more fluid thanks to direct interfaces which will allow enormous, seamless information transfers, humans on the whole will be like a cell is within our bodies, alone its just a cell, but in terms of the species together we'll be a single organism nearly of capability to shape our world at levels we can't now imagine because our information transfer is too clumsy, and slow. Just like early farmers couldn't forseehow a society like Rome could function, because they didn't have codified written language, and just like how a Roman couldn't foresee us with our instant transfers--we will probably be shocked at what a world looks like that allows us to share our thoughts directly, no misunderstandings or imperfections in communication because your meaning is absolutely clear, and you can work with others in the seamless way you move your own hand.
