"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."