The namahage tell the parents that if they clap three times at any time of the year, the namahage will come back down the mountain for the children.
All in all, if I was a small child, I would be very scared. There are recordings in the Namahage museum of the actual event on New Year's Eve and the children are terrified.
The word namahage is thought to come from the word namomi (heat blisters) and the word hagu (to peel). At first, Namahage came after lazy people and would say, "Have your blisters peeled yet?" This was because a lazy person would sit by the fire all winter and get blisters. Basically, the tradition was made to discourage people from being lazy.
The legend behind the tradition goes that the Han emperor (of China) brought oni to the Oga area and they would steal crops and women. The citizens of Oga made a deal with the oni. If the oni could build a stone staircase of one thousand stairs in one night, they would give up all their women. If the oni failed, they would have to leave Oga and never return. Once they reached the 999th step, a villager imitated a rooster crowing at dawn, and the surprised oni fled and were never seen again.
This tradition is only practiced in the Oga Peninsula region of Akita Prefecture in Japan. The words spoken by the namahage are in the Akita dialect, but even more specifically, the Oga dialect. There are traditions like it in Japan and around the world, but the specific namahage tradition is only found in Oga.