The phrase "real credibility" refers to the genuine or authentic belief that someone or something is trustworthy, reliable and capable of performing as expected. It is a measure of the trustworthiness or reliability of a person, organization, product or service. When someone is said to have "real credibility," it means that they are perceived as being honest, sincere and capable of delivering on their promises. In other words, it is a measure of their reputation and the level of trust that others have in them.