"Mochi" is steamed rice cake and "tsuki" is pounding in Japanese.
Mochi-tsuki is a Japanese traditional event in preparing for the New Year.
Mochi is made of glutinous rice which literally is a rice before you pound it. Having it been pounded for a quite bit of time, it turns into mochi, a sticky rice cake, the mochi you know.
The reason of Japanese people preforming mochi-tsuki goes back to Heian Period. It is said in Japan, that God reside in mochi. Rice-cake offering has been a traditional event here in Japan for quite a long time. There are no problem in offering mochi you buy in grocery stores, but Japanese people make mochi from the rice, from the frist step, to show appreciattion toward God for the spent year and also hope for another auspicious year.
Maybe some of you have seen this, "Kagami-mochi". The most popular type of mochi seen in the New Year.