Addresses in Tokyo confuse western visitors. Numbers were assigned chronologically when the house was built.
The Japanese addressing system is based on areas, subdivided from big to small. There are different types of sub-divisions in different areas, but in general, the country is divided into to (都), (capital), for Tokyo, dou (道), (territory), for Hokkaido, fu (府), (metropolis), for Osaka and Kyoto, and ken (県) (prefectures), which covers the rest of the country.
The prefectures (ken) are divided into counties (gun (郡)) or cities (shi (市)). Small cities are generally divided into chou (町) (towns or villages in the dictionary, but maybe areas or neighbourhoods would be better). Big cities are divided into ku (区).
Wards are divided into chou (町) (though sometimes the name doesn't include the word chou). Sometimes the chou are divided into choume (丁目), which are numbered divisions of a chou. Then the blocks are numbered and, at the lowest level, the building has a number. Finally comes the room or apartment number.
The buildings within a block are either numbered in the order that they were built, so they jump all around, or numbered in clockwise order around the block. In this clockwise numbering there is sometimes skipping of several numbers for later assignment, where future construction between existing buildings is possible.