Nonce
A number used once — in mining, the counter grinded to satisfy the target; in encryption, a value that must never repeat for a key.
In simple terms
Miners change the nonce and re-hash until the block qualifies. In encryption, reusing a nonce with the same key can destroy confidentiality.
Analogy
A lottery ticket number: keep scratching new ones until you win — and never issue the same serial twice on the same key.
Going deeper
Bitcoin's 32-bit nonce space is too small for modern hashrates, so miners also vary the coinbase extraNonce (which changes the Merkle root). AES-GCM nonces can be random or counter-based but must be unique per key — libraries enforce this so you never have to think about it.
Common mistake
Treating "nonce" as one concept with one rule: mining nonces may repeat forever; encryption nonces never may.