The Buffalo dance ritual is a ceremonial act of the Mandan tribe, which was located in today’s North Dakota. In former times, this dance was performed in order to honor and worship the spirit of the buffalo, mostly before the start of the buffalo hunting season. Nowadays, it gets danced to ensure the preservation of Native American cultures and traditions and also as a symbolic act for the spirit of the buffalo. A new year’s festival, the so-called Okeepa ceremony, took place so the participants could show their gratitude for the gifts that the First Creator gave to them. The First Creator is part of Mandan’s original tales. They believe in the story of Lone Man and the First Creator, who is also just called “Coyote”. According to the tale, they split up the work of the creation of the world between them.
However, at the beginning of the Okeepa ceremony, the Buffalo dance was performed. The buffalo is still a very important animal for the Native American tribes. However, in the past, it was even more significant since it was the source that provided the tribe members with clothing material (fur), meat, and even tools (bones). As is the case in many indigenous tribes, all members of the community get included in big ceremonies like the Okeepa festival. Female tribe members are responsible for the calling of the buffalo in order to lure the buffalo herd to their hunting territories. During this activity, the men prepared the area where the ceremony takes place. Also, the children were included in the ritual by cleaning the floor of the ceremonial area. This was seen as a symbol to get rid of the famine spirit.
Just as with many religious ceremonies, at one point, the Buffalo Dance was forbidden by the U.S. government. Only after 1978, when there was the American Indian Religious Freedom Act, were people able to attend the Buffalo Dance at big Native American festivals, similar public ceremonies, or private performances.

In order to prepare for the Buffalo Dance, which lasted four whole days, the participants fasted and did not even drink water or sleep. Also, they got purified by sitting in a sweat lodge, where they sweated out every impurity.
The ceremony started with eight performers who were purified and dressed up as buffalos. The sound of drums accompanied them. In addition, they were painted black, white, and red, and they held a rattle in one hand and a rod in the other. On his head, they wore some branches of a willow tree tied to a wreath. The dancer told a story about the buffalo and displayed the animal like it is found in the prairie. As the four days came to an end, a male tribe member entered the camp who was dressed up as the spirit of famine. Eventually, he got scared away by young tribe members. This should symbolize that the tribe will not fear hunger because of the food source that the buffalo provides.

Furthermore, nowadays, the Buffalo Dance of the Mandans gets performed as a part of the Sun Dance ritual, but in former times, it was also included in the Okeepa ceremony, which is considered to be the prelude to the Sun Dance.

Sources:
https://www.worldhistory.org/article/2284/mandan-buffalo-dance/
https://en.wikipedia.org/wiki/Mandan