What is atmokinesis?

What powers did people believe witches have?

This depends on the time and location you're specifying. Witches were (and are still) believed to practice all around the world and through many different time periods. Throughout history, witches have been thought to have power over almost everything, particularly weather (atmokinesis), animals (zoopathy), and physical objects (telekinesis). In the Colonies around the time of the Salem Witch Trials, people were persecuted as witches for their believed abilities to control agriculture, the weather, and their ability to commune with spirits or the Devil. They were thought to be able to use animals, particularly cats, to do their bidding and some people believed a witch could transform him or herself into an animal. In popular culture (TV, movies, books, etc.), witches have been portrayed in every possible way, and it is possible to find a witch in this fictional category that is capable of anything you might think of. Some popular themes are telekinesis (the ability to move things with your mind), telepathy (the ability to read minds/hear thoughts), the ability to cast spells/charms for either good or evil, precognition (the ability to see the future), and many more. If you're interested in this type of witch, I would suggest watching Charmed and Buffy the Vampire Slayer (particularly seasons 4-7), and reading the Beautiful Creatures series. If the real religion of Wicca interests you, there are a wide variety of practicing Wiccans and Witches who believe they have power over certain elements of the natural world. From what I've learned, these powers are gained through practice and focus, but are also sometimes genetic in nature. Some believe they have only the ability to commune with nature and feel at one with the Earth. Others believe they have the same powers you might see in a popular culture witch. In between is a spectrum of different powers, whether real or perceived, which people who claim to be witches can have. I highly recommend looking up some websites or reading some books created by Wiccans or witches, as they can be very enlightening, whether you believe in "magic" or not. Basically, the traditional witch is capable of anything. There is nothing that a spell, incantation, or charm can't do, which is why most fictional witches live in worlds with rules that limit their powers. For example, in the world of Charmed, the witches cannot use their powers for personal gain, or they backfire on them. In Buffy, Willow cannot use her powers to excess or she becomes addicted to the magic. I hope this helped a bit!