Animisim is a kind of religion in which people believe that various non-human things (whether living or not) have spirits. Animists believe that these spirits have an impact on what happens in the world.
Most animistic religions are associated with what we would call "primitive" societies. These are societies which lived in close and constant contact with nature and who therefore felt that natural things had an impact on their lives. These would be people who believed in the spirits of rocks and trees and wild animals and would conduct rituals to appease or propitiate these spirits.
There are "modern" religions with animist aspects. A major one of these is the Shinto religion of Japan. True believers of Shinto believe that many natural things have spirits known as kami. Believers would do rituals to honor the kami and to invoke their aid.
Animism refers to the belief that non-human entities are spiritual beings, or at least embody some kind of life-principle. Animism encompasses the beliefs that there is no separation between the spiritual and physical (or material) worlds, and souls or spirits exist, not only in humans, but also in all other animals, plants, rocks, natural phenomena such as thunder, geographic features such as mountains or rivers, or other entities of the natural environment.