Proof of work is the mechanism that lets strangers agree on one history without trusting each other. The idea predates Bitcoin — Adam Back's Hashcash (1997) used it to fight email spam — but Satoshi used it to secure a ledger.
The asymmetry
Finding a block hash below the target takes, on average, an enormous number of attempts. Checking it takes one hash. That asymmetry is the trick: work is expensive to do but trivial for any node to verify.
Longest chain = most work
Nodes follow the valid chain with the most accumulated work. If two miners find blocks at the same time, the network temporarily splits; the tie breaks when the next block is found on one side, and the other block is orphaned.
Security through cost
To reverse a payment, an attacker must re-mine that block and every block after it, and overtake the honest chain. This is why each extra confirmation makes a transaction safer. The cost is real-world energy and hardware, which can't be faked or printed.
Difficulty adjustment
The target adjusts every 2,016 blocks via the difficulty so that average block time stays near 10 minutes. More miners → harder puzzle. Fewer miners → easier.
Cost as identity
That same cost resists a Sybil attack: you can't flood the network with fake identities and outvote everyone, because influence tracks real work — not how many accounts you open. Every valid block is a receipt that energy was spent, and any node can audit it without asking permission.