One of the things missing from many characters of fiction is mystery. Often, authors reveal too much. They explain every action, every dialogue, every relationship and circumstance. It's generally good to flesh out a character to some extent, but a little mystery goes a long way in making characters interesting and believeable.
It's like the one locked door when all other doors are open. Curiosity is an attractive force. When we're denied access to an area, we want to know what we're missing. And when the light are out, our imaginations replace the light with guesses.
If a character refuses to talk about something, we wonder why. If a character momentarily acts contrary to his or her usual personality, we wonder what we're not seeing and our imaginations race.
Sometimes, it's good to build tension like that and then allow the audience to find out how truth compares to their theories. But real persons always have a little touch of mystery, and I think audiences connect most strongly with fictional characters that are never fully explained. The mystery has to be smartly placed... there are certain things the audience will feel they have a right to know. But don't give them everything, no matter how hard they plead.