That's perfectly understandable, I think relatively few people looked at proof-of-work in detail. I can give you a quick overview of how proof-of-work works (I understand it well enough to actually be able to do it by hand on paper), but nevertheless doing your own research always helps:
To "mine" a block, a miner attaches a random number to the content of the block (the content mostly being the actual transactions), performs a difficult calculation on the entirety (i.e. block and random number), and checks whether the result of that calculation matches a prescribed goal. The goal is to have at least a certain amount of leading zeroes in the resulting number, and it is (to everyone's best knowledge) impossible to know how many leading zeroes there will be without performing the calculation. That is the literal goal, not an analogy.
In the massively overwhelming majority of tries, this goal is not reached. The calculation was useless, and the miner tries again with a different random number attached to the block. There is no other value to the calculation than to reach the arbitrary goal. If the goal is reached, the miner has won the lottery: All participating nodes in the network accept the result (the calculation is easy to verify) and the miner may claim the rewards for themselves.
The amount of leading zeroes to achieve is directly tied to the mutually agreed upon "difficulty". If mining becomes easier and the lottery is won too quickly (say because new faster ASICs flood the market, or more miners participate), the network adjusts the difficulty up, meaning more leading zeroes, so that the overall chances of winning the lottery within a given time frame stays stable.