What is the nonce, and what is mining / Proof of Work?

The nonce is a number miners keep changing until the block's hash meets a target (for example, starts with a required number of leading zeros); finding that number is the "work" in Proof of Work.

The network sets a puzzle: the block's hash must satisfy some hard condition, such as beginning with four zeros. The only field a miner is free to change to alter the hash is the nonce (a "number used once"). Since a hash is unpredictable, there is no shortcut — miners must brute-force it, trying nonce = 1, 2, 3, and so on, hashing the whole block each time, until one produces a hash that meets the target. That trial-and-error search is mining, and the proof that a miner did it is the valid hash itself — anyone can instantly verify it by hashing once, even though finding it took enormous effort. The difficulty of the target sets the block time: make the puzzle harder and blocks come more slowly; make it easier and they come faster.

Go deeper:

• Proof of work — Wikipedia — how the nonce search, difficulty target, and cheap verification fit together.