Its called nahualli in classical Nahuatl and nagualism in more modern practices. The concept of you having an animal that shares it’s soul with you. Sorcerers (brujas y brujos) can transform into the animal that shares their soul [nahualli]. They resemble the concept of a personal totem and shamanic magic.
To Mesoamericans and modern Natives of Mexico animals are really important in magic. In traditional Aztec thought everyone has a nahualli, animal that shares it’s soul with you. However, a good sorcerer can obtain more nahualli. Though it will never share it’s soul like the one you were born with. You can obtain other nahualli through ritual, by stealing someone else’s nahualli, or as a gift from the gods.
One sort of ritual to get another nahualli is to hunt, kill, and eat what animal you want. By eating the animal [or even a person] in magical thought was to “take it’s power” for yourself. [Think you are what you eat.] Life sustained on life, the cycle continues.
Animals are so important in magical thought amongst the people of Mexico that where you’re places on the social ladder would have to do with your nahualli. The frequently seen animals [mice, skunks, pigs, cows, rabbits, etc] by humans represent commoners. Regular folk that make up the majority. The uncommonly seen animals represent the middle class [coyotes, ocelotls etc]. The most powerful people on the social ladder [noble/ruling class] and the most powerful sorcerers are the infrequently, often times nocturnal, animals. [jaguar, owl, bear etc] The most powerful and elusive of all these animals being the jaguar who is held at the highest level amongst most people in ancient and modern Mexico. Anybody with the born nahualli of a jaguar is thought to be endowed with being a powerful sorcerer and skilled at magic naturally.
A “witch” is defined as a person, usually female, who only uses magic to harm. Most people use magic to cure, but also use witchcraft [harmful magic] and curing. These people are usually identified as curers and their practice is past done to apprentices.
Practices and beliefs have the beliefs of Catholicism mixed in with PreColombian beliefs of Natives, such as the Aztecs and Mayans. This happens in rural Mexico.
To Mesoamericans and modern Mexicans reality is an appearance. Any sorcerer/witch/skilled magic user knows that there is layers of reality under this one. That’s why there is 9 layers of the underworld and 13 layers of the heavens. While the main cormos is consisted of earth, heaven, and the underworld. [Earth is middle, underworld below, and heaven above.] Most of magic in Mexico and pre-colombia Mexico used the practice called dream working. Where you use your dreams to manipulate reality, gather information, or cure someone and so forth. Rituals may take place in the waking world, while the rest takes place in the other one, the realm of dreams, where the sorcerer or curer can travel to the underworld if needed. Caves, mirrors, and water are thought to be portals in this otherworld. If one can’t travel to the underworld or otherworld in dreams, one would do a ritual in a cave or the cave’s entrance for example.
The appearance of reality, layers of realities with in reality, is perhaps a very important part of magical practice. Trickery and illusions in Mesoamerican magic is very much used and valued. The god of sorcerers himself, Tezcatlipoca, often used trickery, which included appearance based magic to get what he wanted. [His nahualli is also a jaguar] These types of things are a good skill to learn if one travels to the otherworld or underworld, as one would encounter demons and spirits with ulterior motives. Also, stealth is a skill to be acquired so that one would not be seen by beings that might harm one.
In theory one can influence reality through the otherworld. Like a ripple effect when you through a stone into water. In the dream world you can turn into your nahualli, become in tune with it, and use its skills. This is especially useful if you have a flying type nahualli, which can go into the heavens better and travel at a better speed.
Animism is a concept, that everything has a spirit. Even inanimate objects. This is useful in incantations where you state your intention and will. Its how you make objects yours and how you direct their energy, as well as purifying.
Amongst the otomi it is thought that you should do your best not to influence people too negatively, because you may attract the attention of a witch. That is you should blend in.