For example, I'm a linguistic consultant working in the NLU processes of a modern search engine. I'm a tiny, miniscule cog in this colossal contraption, one of multiple thousand linguists and engineers. Only my immediate team knows almost exactly what I do. Colleagues from contiguous teams in the same NLP project will have a very broad notion but won't be able to follow any details unless I spend hours training them first. Vice versa, on both instances - it's not because I'm oh so smart, but because being ultra-specialised is the nature of the job.
Now, the above is between professionals still within the same company, same project, and same expertise of computational linguistics. Which is just one out of dozens, maybe hundreds of different technical disciplines within the broader IT/CS field. Like, my grandmother cannot even begin to understand the potential of a computer beyond "super calculator", to the point that she thinks I'm lying when I say I'm working because if I'm looking at the computer then I can't be that busy (true story lol). I can't really explain to her how a computer is able to process extremely complex data to accurately model, say, a biological structure and then run projections on it to test out improvements, because my nana cannot even conceive that it ever could. She's so far removed from it that it's effectively beyond her intelectual grasp.
So my question is... has there ever been, historically, a tool with such immense scope? With this much potential to improve human understanding, but also so complex that at the highest degree it took/takes almost hive-like levels of specialization to pull off?
It is important to remember that before a computer was a warehouse-sized electromechanical device, before it was a box on the desk of every home, before it was powering your smartphone and your fitness tracker and in your car and everywhere else... a computer was a human being.
From a historical standpoint, when your grandmother thinks of a computer as a "super calculator" she is essentially correct. All the complex modeling you do, all the spreadsheets, all of that really does boil down to complex calculations which are processed through electronic circuits at a blistering speed.
What made digital computers possible was Claude Shannon's thesis A Symbolic Analysis of Relay and Switching Circuits (1937), which showed that Boolean algebra (which had been around since George Boole's The Mathematical Analysis of Logic in 1847) could be applied to electrical switches - 0 or 1 being equivalent to off/on, high voltage or low voltage - and you can translate pretty much any mathematical calculation into Boolean terms, and away it went.
Before digital computers, however, you had analog computers. These were devices where an electrical signal was used to approximate a complicated mathematical function, usually a time-based one, so that you could project an answer for a given input in less time than it would normally take to compute it by hand. Again, this is still when the term computer normally referred to a person, maybe one with an abacus or a slide rule or an expensive electromechanical apparatus that would facilitate the calculations they were making, but for the most part they were rooms full of people tabulating, collating, and processing vast amounts of raw numbers.
That kind of effort seems almost ludicrous to us now, because we have so much computing power at our fingertips, but it is fundamental to our historical understanding of how historical societies functioned and understood things. The sum total "processing power" of the Chinese bureaucracy during, let us say, the Ming dynasty (1368 to 1644) was measured in the man-hours of the Six Ministries. They used plenty of technology - in the sense of developments in mathematical notation, techniques, labor-saving devices (abacuses, etc.) - but you're still basically looking at emperors for which crunching the data to figure out, say, the average production of wheat in a given district over time was process of not just ongoing record-keeping but hours or weeks of time to transfer the data, perform the operation, and translate the answer into terms that make sense.
History is full of a lot of that. Today's digital computers, cloud computing, etc. enable us to do lots of operations vastly quicker than was possible historically - making feasible a lot of operations which would have been cost-prohibitive even a decade or two ago - but the fundamental practice of what is being done is essentially the same as it was a hundred or a thousand years ago.
In terms of hyper-specialization - that's a little trickier. In very broad terms, pretty much every profession by definition requires some degree of specialized knowledge. I don't want to fall into the Sid Meier trap of trying to characterize past societies like we can rank how many specialists they can support based on size and resources or any of that claptrap; it isn't anything that formulaic. Part of what computers did do was open up new careers for folks to utilize the new possibilities that digital computers made available - and again, that's nothing new. You don't have a bowyer before you invent bows; you probably don't have a smith that specializes in making plate armor before your metalworking economy gets to the point where you can produce enough high-quality steel and have enough demand for plate armor and the right financial structures in place to establish armor-smithing as a specialist industry. It's not just a question of the technology being available, if the contemporary society isn't poised to develop or sustain such an industry. It's not like the world didn't have mathematicians before ENIAC (1945), but there probably weren't a lot of people that could be mathematicians full-time in every historical society.
Even once you have a mature industry with specialists...there's no guarantee that specialization is going to remain relevant. The demand for plate armor in Europe drops a bit as firearms become increasingly more prevalent in warfare. It's not that any of the relevant underlying technologies are lost - if anything, steel production gets better - but the underlying socio-economic circumstances that supported the armor-crafting industry shift.
Okay, so the historical examples are getting a little ways away from me, but you can also see this in how older coders age out as new programming languages and coding paradigms take over. And probably if your nana sat down and pressed you, you couldn't explain every part of the process of what you do either. That's a function of how complex contemporary systems are, but it's also an expression of how complex data processing and manipulation has always been - there have always been "cogs in the machine," even if they were flicking beads on an abacus and recording the data. What they were processing and how that affected their world was something a lot of the human computers couldn't know, and to people who had no idea how to write, the idea that one young person working an abacus could result in the government sending famine relief or tracing the orbit of a planet across the sky would have seemed fantastical...but historical societies really did those things.