Local-script rendering is the address written the way its own postal operator prints it in the country's own script and order — prefecture, city, ward, block for Japan; province, city, district, road for China; the largest part first and the building last — where the format table carries such a layout and the address was written in that script.
What Spaw answers
formatted_local carries that rendering for Japan, China, Taiwan, Hong Kong, Macao and the two Koreas when every place part of the address — the street line, a building, the district, the town, the area — is written in Han, kana or Hangul with no Latin word among them; the organisation line may stay Latin. The postal mark 〒 is kept, no uppercase rule applies, a named building stands above the street, and the whole thing is null for everything else: a Japanese address written in Latin letters, a mixed-script one, or any country whose local layout repeats the Latin order, which is the case for the seven other entries the table carries.
What it does not mean
It is not a transliteration. Rendering a Latin-written Tokyo address in kanji would mean inventing characters the customer never typed, so the field answers null rather than guess; formatted still carries the Latin layout for every address. A one-line Japanese address is best sent as separated fields, because the parser reads a single line of kanji as one street.