Although at least half of his work was later discredited by further research, psychiatric pioneer Sigmund Freud laid the foundation for much of what we know about the human psyche--that part of the brain out of which arises the deep emotional motivation for the actions we take. One of the terms Freud coined to describe one of those functions is 'projection.'
According to Freud and most practitioners of modern psychiatric medicine, projection is the process by which a person 'projects' onto another person their own motives, emotions, or intentions which they find to be too detestable or otherwise unacceptable to admit.
For example, suppose a member of a large family of siblings rose to forefront of the pack when their mother became terminally ill. This sibling had the time and the good health to care for the parent, providing around-the-clock care at a time when it was impossible or very difficult for the other siblings to do so.
At times in these cases, some families can grow vicious. Suppose, in this case, that a sister to the sibling who is providing the care stated the following: "She's up to no good. Just look at her. Doting over Mama like that. She's doing it only so she can manipulate Mama to change her will and give her most of the estate."