Kagami mochi (鏡餅, literally mirror rice cake) is a traditional Japanese New Year decoration, which consists of two round mochi (rice cakes), the smaller placed atop the larger, and a Japanese bitter orange, known as a daidai, with an attached leaf on top. It may also have a sheet of konbu and a skewer of dried persimmons under the mochi.
It often sits on a stand called a sanpō (三宝, see photo below) over a sheet called a shihōbeni (四方紅), which is supposed to ward off fires from the house for the following year. Sheets of paper called gohei (御幣) or shide folded into lightning shapes are also sometimes attached.
Kagami mochi first appeared in the Muromachi period (14th-16th century), the name kagami ("mirror") having allegedly originated from its resemblance to an old-fashioned kind of round copper mirror which also had a religious significance.
The two mochi discs are also said to symbolize the going and coming years, the human heart, yin and yang, or the moon and the sun. The daidai (橙), whose name is synonymous with "generations" (代々), is said to symbolize the continuation of a family from generation to generation.
Traditionally, the kagami mochi was placed in various locations throughout the house. Nowadays, however, it is usually placed in a household Shintô altar, called a kamidana or placed in a small decorated alcove, called a tokonoma, in the main room of the home. (Once again, adapted from Wikipedia's entry.)
The kagami mochi in my home.
At a small privately owned shrine in the neighborhood.
At Kego Shrine in Tenjin, Fukuoka.
The neighborhood mochi shop at the end of the year.
Fresh mochi rice cakes.