What is lending of credibility?

"Credibility" is the state of being believable. An authority or statement a person is likely to believe has a lot of credibility. Sometimes other factors make such a source even more believable; in that case the other factors are said to "lend credibility" to the original statement or source. This means the same as to "add credibility".

E.g. "I generally believe what Mr. X says about unemployment, and this recent report lends credibility to his statements."