A unique number, assigned by manufacturer, for some produced part, item or product. Also found on paper money.
For physical objects, this is often just a number that starts from 1 and continues forward with increment of one. Personally, I have one item with a very low serial number (my HardSID card with serial number 00037.)
For some products, such as computer programs, it often also includes some sort of checksum or other special identifier. (This is common in case a proper serial number must be entered in order for the item to be operated; a simple serial number may not be enough.) See also CD key.