to write or say something in order to make the true facts known.
"She's decided to write her memoirs to set the record straight once and for all."
Celebrities or public figures often go on TV after vicious rumors are spread about them, in order to set the record straight. I'm sure there are a few that you can think of off the top of your head who should probably make a public statement in order to set the record straight.
Can you think of a time when you needed to set the record straight?
Definition from Cambridge Advanced Learner's Dictionary and Thesaurus.