I am not too familiar with animism either, but as far as I understand from the book, it's the belief-idea-philosophy that humans are a part of nature, including both living and non-living things. (Contrary to modern idea of separating the "human" and "natural" worlds). In addition to awareness and careful choices, it believes in reciprocity, giving back what was taken from the ecosystem. Similar to what was/is practiced by many native communities.

(Please correct me if I am wrong)