Nonce is an abbreviation for “number only used once”, a single-use arbitrary number generated to prevent replaying past transactions.
During the mining process, nonce is a number added to the hash output by the miner to make it have a low value or equal to the mining objective. To generate a hash target that starts with the number 0, miners can only guess the nonce numbers. So, one could say that nonce is a brute-force method of achieving mining goals.