Dalai Lama Asks -- "If Buddhist Doctrine of 'No-Self' Is Wrong, Who Are These People?"
Anatta says that personal identity - the self - is actually an illusion. Instead, each of us is an aggregation of different factors (biological, historical, karmic, experiential, etc.), intersecting to create the false sense that we exist as distinct beings. The Buddha compared the self to a chariot: Is the "chariotness" in the wheels, the axle, the seat ... or not in any single place at all?