The phrase 'give the benefit of the doubt' means to regard somebody as though their behavior is right, despite the fact that you are not sure that it is.
Example of use: "I think that he broke his glasses on purpose, but, I will give him the benefit of the doubt."
This is a known English and American legal term. This term was first used in Irish treason trials in 1798 where the defense stated that “if the jury entertain a reasonable doubt upon the truth of the testimony of witnesses... they are bound” to acquit.