Answer:
They are portable tissues!
We have handkerchiefs as well, however, we have them mostly for the sake of wiping our hands after washing them. When we blow our nose, we mainly use a tissue paper rather than a handkerchief. At kindergarten or elementary schools, teachers let students have both a portable tissue and a handkerchief as one of manners they should have.
If you hang around a city in Japan, you would probably see people handing out these portable tissues for free. In Japan, portable tissues are popular medium for advertisement. On it written is an ad of a store or service such as Karaoke, bars or English schools. A Price of printing companies offering is around from 5 to 15 yen per a portable tissue.
In Japan, there has been a counterpart of tissues called “chirigami” since early times. It is a rectangular paper, and rougher. This was used both when we do the business, and blow our nose. School kids in those days used to have folded chirigami in their pockets at school.
After the WWII, as western cultures were introduced into Japan, tissue papers, which had been invented before the war in the United States, and toilet papers, which had been already popular from late 1800’s in Europe and the United States, were introduced into Japan. Through 60’s, when Japanese companies started manufacturing tissues, and invented portable ones in Japan, the roles of chirigami became covered by tissue papers and toilet papers, and meanwhile chirigami became out of use.
Incidentally, we used to use “tenugui”, a traditional cloth we have had fore more than 200 years, to wipe our hands, or wipe our body. However, during a cultural enlightenment time in the 19th century, towels and handkerchiefs were introduced into Japan, and they covered the both uses of tenugui. This is why handkerchiefs are mainly used to wipe our hands in Japan.
I, as a one of Japanese, don’t feel like
blowing my nose with a handkerchief and put it back to my pocket after because if
I blow my nose with a handkerchief again and again, the handkerchief gets
dirty, and it would dirty my pocket, too! To avoid this, I use a tissue paper,
and throw it away.