The Collective Unconscious is a term coined by Carl Jung that refers to unconscious material that is shared by all humans. It contains instincts and archetypes (primal symbols that show up in people's dreams and hallucinations,) and underpins the individual unconscious. It is inherited by all people—it is the common soul of humanity.
The Collective Unconscious is identical in all individuals, and is said to contain all of the psychic material of our ancestors all the way back to the beginning of human life. It exerts an influence over our unique consciousness that tries to pull us back to our primitive human ways, an influence that lessens as we go through the process of individuation.
Jung was very much an empiricist, and based almost all of his science of the psyche on personal observation of his clients over the many years he spent as a psychotherapist. He was very interested in dream images, and developed his ideas about the archetypes primarily from the recurrent images of characters that showed up in his patients dreams. My goal here is not to discuss the archetypes at length, but I would be remiss if I didn't mention that they play a significant role in Jung's understanding of the Collective Unconscious. These images showed up again and again in clients who had no idea what they meant or where they came from. Jung believed that the archetypes that showed up repeatedly for individuals were budding personalities within an individual psyche, and that each of us has personal archetypes that have something important to teach us about ourselves.
The benefit of recognizing the Collective Unconscious and understanding its power is realized when one diminishes its power. Take, for example, a person who has recurrent dreams involving the Witch archetype, and transfers their bad feelings about the Witch to real people in their lives. If they consciously hold the archetype in mind, talk to the archetype, and uncover a specific person from their past associated with that archetype, they strip the Witch of its power to influence their behavior. They will no longer project those bad feelings onto others, and are free to develop happier and more satisfying relationships.
Jung described his evidence for the existence of the Collective Unconscious as empirical, and its nature creates a problem for any attempts to prove its existence. Because the Collective Unconscious exists outside of the conscious reach of the mind, there is no way to inhabit it consciously or design experiments to prove or disprove its existence.
Want more? Check out verywellmind.com's write-up on the Collective Unconscious.