The nonce in a Bitcoin block is a 32-bit (4-byte) field whose value is set so that the hash of the block will contain a run of leading zeros. The rest of the fields may not be changed, as they have a defined meaning. Nonce is an acronym for "number only used once" and therefore is a random number you can use only once -:). Nonce is the number that blockchain miners try to solve to get the block reward whilst the number of zeros that the hash must start with corresponds to the "difficulty" of the puzzle that must be solved.
