It means that if the components (metals) in an alloy could be segregated out of the mixture and were then divided into 1000 equal mass parts, then 955 of those parts would be a specific metal. Usually that specified metal is a precious metal such as gold, silver or platinum. For example, "sterling silver" contains 925 parts of pure silver in the mix, so sterling is 925 fine. "Pure" silver would be "1000 fine" but the number of 999 is the generally accepted number for purity.
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