(verb)
to have trust or confidence in someone, to the point of being willing to share private/secret matters with them;
e.g. He will confide in his brother, since the two are very close.
(verb)
to give some object to someone (i.e. to entrust it to them) so that they can look after it, to have the confidence/trust in someone to allow them to protect or care for something;
e.g. I will confide these documents to them for safekeeping.