To confide in someone is to tell them something privately. We confide in people we trust.
We all have secrets and subjects that are hard to talk about. When we want to talk about something sensitive, we look for someone to confide in: a person we trust not to blab about our business to the rest of the world. Most people confide in close friends or family, often to get advice. If you tell someone a secret, and then they tell ten of their friends, you made a mistake by confiding in that person.