There are different ways to think about it, but I find this the most illustrative. Mining is about authorship of the blockchain. The system is simple enough;

There are different ways to think about it, but I find this the most illustrative. Mining is about authorship of the blockchain. The system is simple enough; people broadcast transactions, and they get collected and entered into a shared ledger. But the details are tricky. Order is one major issue; does A or B come first? A and B may be mutually exclusive, so whichever is first is critical. Because the network is imperfect, and network users may be malicious, it is very important that we come up with an extremely robust way of deciding how transactions are entered into the blockchain. Authorship - that is, mining a block - is everything. The simple solution is to make it random. If it's random, then no individual miner can reliably control authorship, and thus cannot engage in attacks like double spends (unless they control a majority of the mining power, i.e. a 51% attack). POW is a way to achieve randomness in a robust way. The only way to mine a block is to solve a problem that can only be solved via brute-force hashing. This is costly to do, so incentives are offered to get people to do it via coinbase rewards and transaction fees. This adds to the security model because miners now have strong economic ties to the POW algorithm and blockchain with capital and marginal costs. Of course, there are other ways to achieve randomness, but can you think of one that will force a decentralized network to achieve robust consensus (i.e. to not fork)? Much of the 'magic' of Bitcoin comes when you realize the incentives under which miners operate. Once a valid block is broadcast on the network, miners have extremely powerful economic incentives to accept this block and begin mining on top of it. Consider what happens if, instead, the miner continues to mine at the 'old' block height. They may come up with a valid block fairly soon (it's random, so they have no way of knowing), but each moment that passes, the other miner's valid block is being transmitted over the network. Any subsequently transmitted valid solution is at a disadvantage in becoming the consensus, and that grows as time passes. Basically, any time spent mining on the old block once a valid one has been seen is pure waste. Since the entire network operates from these same incentives, consensus grows very strongly as no one wants to mine on a minority chain. _____ Difficulty is a different issue; this is just a way to keep block times fairly consistent, even as the network grows and more mining power comes online. Because it is calculated directly from the block chain, difficulty rules follow the same strong incentives that build consensus on the majority chain.