What it is
Projection is “the mental process in which an individual attributes their own internal thoughts, beliefs, emotions, experiences, and personality traits to another person or group.” Freud first described it. In its defensive form, you push something you can’t accept in yourself onto someone else: you’re angry, so they must be the angry one.
There’s a milder form too. Some psychoanalysts see projection as the root of empathy: you use your own experience to understand someone else.
How it shows up for me
I once asked myself, “I projected? I saw myself in her. Is that the same?” Not quite. Seeing yourself in someone can be projection, or a real recognition. The test is contact: spend more time with the person and see if what you saw is still there.