Animism, in basic terms, is the belief that a soul exists in all things, from humans to stones. This religion also entails the belief that a person can impact the land where s/he lives as much as the land can impact the person. Another fundamental belief of animism is that everything coexists for a greater purpose, rather than the purpose of an individual.
While it is believed that primitive animistic beliefs have existed in people since the Paleolithic era, actual anthropological proof has been found that shows aboriginal Americans practicing animism. British anthropologist Edward Tylor believed that early Americans described a soul as a vaporous gas that could pass from being to being. Tylor also believes that souls and animism were used to explain sleep, dreams and death.
An excellent explanation and example of animism can be found in Daniel Quinn's book, The Story of B. Here is an excerpt from The Story of B where the misconceptions surrounding animism are talked about:
"...Most people in my position, with my training, are aware of animism the way modern-day chemists are aware of alchemy."
"You mean you're aware of animism as a crude and simplified precursor of religion the way chemists are aware of alchemy as a crude and simplified precursor to chemistry. Not really a religion in the proper sense any more than alchemy is chemistry in the proper sense."
Sources used:
http://www.themystica.com/mystica/articles/a/animism.htm
http://hpwsys.com/dave/