Let’s start with a simple database on your PC - only you can edit it. You want everyone to participate it instead, so you make it peer-to-peer. Of course, it ends up as a total mess, with people deleting what others have written. So, you make it append-only, so you cannot edit what has been before. But it’s still a complete mess. Now, you restrict who can append to it, and their additions need to be verified by everyone else, and now it finally makes some sense. This is consensus, but local consensus. The next question then becomes, how can you retain this pattern, but start making it more accessible once again, like it was before?
The answer is - you make it expensive to gain the rights to append your own block. On Bitcoin, it’s practically impossible, so you need a) an industrial operation with hundreds of millions of dollars, b) collaborate with other such industrial operations to collectively produce a block. On Ethereum, the above applies, but there’s also a side channel where you can stake US$75,000 for the privilege of appending a block once every 4+ months on average. On top of that, you stand to lose most of that stake if you’re malicious. There are other mechanisms, but either way, the goal is to make it very expensive.
Why so expensive, then? It’s the only known objective method to deter block producing participants from corrupting the network. The more expensive it is, the greater the deterrence.
By following this method, this new database - let’s call it a blockchain - can achieve strict global consensus, where everyone agrees on the same block in real-time. Different networks achieve finality in different ways, but once it is achieved, the job of the blockchain is done. Indeed, this is the only job that blockchains can uniquely do. From here on, you can discard the blocks from this network - as long as there’s one copy it’s all good.
However, there’s a caveat. This is extremely centralizing. No matter which mechanism is used, this is effectively a plutocracy, where a few of the wealthiest people in the ecosystem can collude to control the network. In the case of Bitcoin, the economies of scale for mining are very powerful, and with dwindling subsidies over time, it’ll inevitably be down to an oligopoly of a handful of highly industrialised mining operations and maybe a couple of mining pools doing all the block producing - effectively a corporatocratic dystopia.
So, you have achieved strict global consensus, but in a highly centralized manner.
This is where you need a last line of defence, and it comes in form of subjective rough global consensus. A public blockchain network is ultimately formed by node operators who are not producing blocks. It’s not free - as you need a computer and the knowledge to run the node - but it’s accessible. The cheaper and easier it is to run a node, the more independent unsubsidized operators there are, the stronger the rough consensus.
In very rare occasions, the objective strict global consensus formed by block producers diverges from the subjective rough global consensus formed by the node operators. The canonical chain is always determined by the node operators. So, the objective strict global consensus is thus conditional on the subjective rough global consensus.
I tried to make this post simplified and without nuance, but even so, it’s more complicated than I would like.
The goal should be to invent a better objective method for appending blocks - without losing said objectivity and neutrality - so you don’t need a subjective fallback as much. No idea if that’s possible, though.