What does it mean by the phrase "not my story to tell"

He says, "It is not my story to tell." For some reason he is not allowed to tell the story. Perhaps it would invade the privacy of some third person. He is leaving it up to that third person to tell the story if she wants to.

In addition GEdgar’s spot on response, it can also be used politely to not attempt to take the limelight with a story. For instance, if I was an observer of an incident, and the actor was present, it would be polite for me to introduce the story, and say “its not my story to tell” to give the actor the option to take center stage, or to allow me to tell it if they aren’t the center-of-attention type.