You've probably seen these worn by people in photos taken in Japan. Surgical masks can serve a variety of purposes, and they also come a variety of colors, sizes and designs! The primary reason Japanese people wear surgical masks is to not spread germs, especially if you're sick, this is a big deal in major cities where everyone is in close contact most of the time.
If you happen to be sick, not wearing a surgical mask can be very rude. You're putting everyone at risk, and getting sick can cause people to miss work and other special events. Even if you're not coughing wear a surgical mask if you're not feeling well.
Masks can be purchased at almost all supermarkets and connivence stores around Japan, so theres no excuse for not wearing one!
Showering and Bathing
The way people shower/bathe in Japan is a little different than in western countries, mainly because the two occur together. People take a shower to clean themselves, and then they go into a hot bath to relax.
In a typical Japanese apartment the bathtub, shower, sink and toilet will all be in the same room. The entire bathroom can get wet so don't be afraid to get everything wet. The shower is just a detachable shower head on the wall, you can step into the tub to take a shower.
Once you, and everyone else in your house have taken a shower you fill the tub with hot water. In a typical Japanese family bathing order is based on the hierarchy of the family, with the father going first. The same bath water is used for each member of he family. After everyone is done the tub is drained and cleaned.
Cleaning...Lots of Cleaning
Cleaning in Japan may differ a bit from western societies, particularly because it happens at lot. Japanese homes are always kept in pristine conditions, it's seen as bad morals to have a dirty home. Because people strive to keep their homes clean it's only common curtesy to help them keep it this way.
When you visit a person's home make sure to take off your shoes at the genkan and put on house slippers. When you enter the bathroom put on the bathroom slippers provided, and make sure to take them off before you leave.
Schools are another building that requires the help of all who attend to keep cleanly. At the end of each day students are required to clean their classrooms and bathrooms. On specific days students and faculty spend a couple hours cleaning the school and the grounds surrounding it. This is meant to ingrain cleaning habits in students, and instill good morals. If you plan on teaching at a Japanese school you are expected to help out, so don't try to call in sick!
Why? Religion of Course!
Religion plays a big role on the cultural significance of cleaning and hygiene. The religion of Shinto greatly values purity, in fact you have to wash your hands and face before entering a Shinto shrine. Shinto God's (Kami) are said to hate filth, and since every living ting in the Shinto religion contains a Kami it only makes sense to keep everything clean.
Buddhism also teaches that cleanliness is key to having a peaceful mind and teaches good morals. Even if you don't believe in either religion cleanliness has become ingrained in Japanese culture, so it's best to follow the "rules".