In Japan, the month of December is called "shiwasu (monks run)”. According to one theory, it is called so because "shi," or monks, are busy running to perform sutra chanting at homes at the end of the year.
Here are some of the things that come to mind when you think of December in Japan
Weather
Japan is a small country, but because it stretches from north to south, there is a big difference in December temperatures between Kyushu in the south and Hokkaido in the north.
Nagano and Niigata have a lot of snowfall, with days below freezing.
In Tokyo, it feels warm on sunny days, but in Kyoto, it can be surprisingly cold.
Kegani, Hairy crab from Hokkaido
One of the foods in season in December is “Kegani”, or horsehair crab. It is often served in the New Year's Eve meal.
Horsehair crab contains many nutrients that promote antioxidant properties which boost immunity and relieve fatigue, making it ideal for eating at the end of the year when people tend to get tired and catch colds.
In December, hairy crabs from the Tokachi coast and Hidaka are in season
Winter Illumination
The winter illuminations are one of the main attractions of visiting Japan during the winter. December usually has the illuminations going in full-swing, and you can find showings all around Japan. The winter illuminations are specific places that are lit up in holiday-esque lights that are artfully decorated. Seeing the lights are a popular things to do among couples. The lights also make for a romantic scene perfectly illuminating the dark. Popular and recommended places to go see the winter illumination are Nabana no Sato in Nagoya and Kamakura. You can also find beautifully lit up streets throughout Tokyo, Hakodate, Osaka, and more!
Festivals/Events
December brings a variety of festivals and events, and seasonal activities open up. Of course there is the aforementioned winter illumination events. Depending on the location you may need to purchase tickets beforehand or reserve a spot before going. The Hagoita Ichi Festival is happening in Asakusa and the Chichibu Night Festival, where you can view fireworks in winter, in Saitama. Ice-skating opens up in various parts and is a nice pastime to take advantage of the cold weather. 
Toshi no Ichi (Year-end Market)
One of the events held in December is the year-end market.
The Hagoita Market is a year-end market at Sensoji Temple in Asakusa, which has become famous throughout Japan because of its enormous scale.
Hagoita paddle boards are decorated with gorgeous ornaments, which have been displayed to ward off bad luck and evil spirits.
Christmas
Christmas is celebrated in much of Japan as a holiday. However, it does not hold the same traditions as western countries like the United States. For one, December 25th is considered more of a couples day instead of a family-oriented day. That is not to say that it is not celebrated amond families, only that it is considered a romantic day for couples to spend together. On this day, popular customs and festivities include buying KFC chicken, a holiday cake (usually strawberry shortcake), and going out to see the holiday lights and winter illuminations. It certainly is a very festive time to be in Japan!
December is definitely a fun time to be in Japan. Plenty of events are still happening depsite the cold, and the change in weather also allows for a refreshing look on many landmarks, like Shirakawa-go which may have snow which transforms the village into a cute, winter village. There are many more places to discover that look completely anew, and December can definitely be a good time to visit Japan depending on what you're looking for.
Joya-no-kane
On New Year's Eve, temples begin ringing the temple bell.
The bell is rung 108 times over the course of the day.
It is generally known that this number of 108 represents the number of human carnal desires, and the bell's purpose is to get rid of these desires and vexations to welcome the New Year with a pure heart.