The pool accepts 'shares' of 'close but not quite' values to prove that the client is actually doing work. Then, you had the emergence of marketplaces of hash power -- you could bid on or sell a specific number of hashes a second for a given time. The highest bidder would be able to point your mining hardware at their choice of pool with their payout credentials.
It is in the interests of the miners to prevent a situation where one pool takes a majority of the hash rate. Miners will migrate to smaller pools if one is getting too big.
The best way to learn IMO is to try it yourself with your gaming computer. I personally use a platform called NiceHash (not sponsored, nor am I advocating for them, there are alternatives) which pays out in Bitcoin. Try it out yourself, depending on your GPU you could be making $3-10 per day. Run it for a month or two, or longer. Transfer that Bitcoin to an exchange of your choice (Coinbase, crypto dot com, etc.) and sell it for cash. Then use that cash to buy more hardware (or beer).