proof of work
Proof of work is a way of deciding who gets to add the next block by making it costly to even try. Each participant races to solve a hard numeric puzzle that has no shortcut — you can only find the answer by guessing over and over, billions of times a second. Whoever stumbles on a valid answer first wins the right to publish the next block. It is, in effect, a costly numeric lottery where buying more tickets means burning more electricity.
The puzzle is built from cryptographic hashing. A miner takes the block's data plus a changeable number called a nonce, runs it all through a hash function, and hopes the result comes out below a target value — like rolling dice and needing a number under a tiny threshold. There is no clever trick: the only strategy is to keep changing the nonce and re-hashing until you get lucky. But once someone finds an answer, everyone else can check it in a single instant. Hard to produce, trivial to verify.
This asymmetry is what secures the chain. Because each block embeds the previous block's hash, rewriting an old transaction would force an attacker to redo that block's work and every block after it, faster than the entire honest network is extending the chain — an astronomically expensive task. Proof of work is how Bitcoin lets a leaderless network agree on history: the longest chain, representing the most accumulated work, is the one everyone accepts as true.
block + nonce → hash nonce=1 → 9f3a... (too big, retry) nonce=2 → c10b... (too big, retry) ... nonce=87142 → 0000a3... (below target — winner!)
Keep changing the nonce until the hash starts with enough zeros. Finding it is slow; checking it is instant.
Securing a chain this way consumes large amounts of electricity, which is why some newer chains use proof of stake instead.