Link #1
It's actually called "Hara-maki/腹巻. It can be translated as belly warmers. You put it on around your belly (Please see link #2 below). Generally, we put on belly warmers under our shirts to conceal them. When we put on fashionable ones, we sometimes wear them as a part of fashion. In Japan, letting your belly cool isn't good and can cause you to have a cold, although I don't know whether or not it's true. Because of this traditional idea, a lot of Japanese people care about keeping their bellies warm by wearing belly warmers. Mothers often put them on their small children. Even during summer, some people prefer to wear them while they are sleeping (Belly warmers for summer are made of cotton, and ones for winter are made of wool or acrylic fibers). School girls who want to make their uniform skirts short often wear belly warmers during winter.As you can see, belly warmer are used regularly and habitually by a lot of people, regardless of gender and age.
Link #2
http://hisasann.com/digital/2008/03/post_302.html
You can also see the popularity of belly warmers from a very popular Japanese movie "Otoko-wa-tsuraiyo/男はつらいよ” (please see link #3 below) and a popular manga "Tensai-bakabon/天才バカボン” (Please see link #4 below). Many years ago, since many fathers wore belly warmers, old-time, everyday fathers in movies and mangas were portrayed this way.
Link #3
Link#4