The word ‘nonce’ is used to mean ‘number only used once’. Ethereum has a few different nonces:
Account Nonce or Transaction Nonce: Every account has a nonce that stores the number of transactions that they have sent. The first transaction sent from an account has the nonce 0, the second has nonce 1, and so on, with no repetitions. This is a security feature that ensures someone cannot try to ‘double spend’ your money by replaying a transaction from your account.
Block Nonce: Every block in Ethereum (and Bitcoin) has a nonce. When creating a new block, miners must find a nonce that solves a particular math problem. This takes them a lot of work, and when they find a nonce that solves the problem, they include it in the block as proof. This is where the phrase ‘Proof of Work’ comes from.