Definition 1: True story, has become a phrase of agreement or acknowledgment akin to the phrase 'true that/dat.'
Definition 2: To express an almost disinterest in what someone has said, by simply affirming they have said it. Common synonyms are: cool, gotcha, uh-huh, true that, etc.
Definition 3: It can be used to try to affirm your own statement.
'Obama is doing a pretty good job in the White House so far, don't you think?'
'I just ate an entire pie!'
'I just ate dinner with Britney and she gave me head in the parking lot! True story!'