Someone who is handpicked has been carefully chosen for a special job, not taken at random and not only because they were next. A coach handpicks a team. A boss handpicks a helper. The picture behind the word is picking fruit by hand, one by one, so you take only the good ones — and that older meaning is still alive: handpicked berries, handpicked tea. In everyday talk, though, you will hear it more about people, and it feels like a compliment: they wanted you on purpose.