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 zeros. The rest of the fields may not be changed, as they have a defined meaning.
Any change to the block data (such as the nonce) will make the block hash completely different. Since it is believed infeasible to predict which combination of bits will result in the right hash, many different nonce values are tried, and the hash is recomputed for each value until a hash containing the required number of zero bits is found. As this iterative calculation requires time and resources, the presentation of the block with the correct nonce value constitutes proof of work.
A golden nonce in Bitcoin mining is a nonce which results in a hash value lower than the target difficulty.
In many practical mining applications, this is simplified to any nonce which has 32 leading zeroes (2.1), with a secondary test checking if the actual value is lower than the target difficulty.
The term golden nonce most likely evolved from the term golden ticket as used to refer to a nonce satisfying the mining requirements as early as April 8th, 2011 (3.1)