What does it mean to give credence to something

I cannot give credence to his account.Britannica dictionary definition of credence.[=i generally do not believe statistics] don't give credence to [=don't believe] their gossip.Give credence to (someone or something) to make something seem more credible or probable, perhaps by providing additional information or details.This new evidence gives/adds/lends (some.

Confidence, faith, stock, trust, belief, credit;Credential (esp in the phrase letters of credence ) 3.Something supporting a claim to belief;If something lends or gives credence to a theory or story , it makes it easier to believe.Acceptance or belief, esp with regard to the truth of the evidence of others.