The phrase is quite literal, "benefit"... something given as a gift "doubt"... disbelief I'll give you the gift of not believing. Example: If someone has been shot and you find your friend with a smoking gun in their hand. anyone else would believe that they were naturally the shooter but you "give them the benefit of the doubt" and let them explain why they have the gun. It's also commonly used as "Even if I gave you the benefit of the doubt, " meaning that there is no way it isn't true. "Even if I gave you the benefit of the doubt that you found the gun, what were you doing in his room?".

to decide you will believe someone or something to believe something good about someone, rather than something bad, when you have the possibility of doing either e.g : After hearing his explanation, I was prepared to give him the benefit of the doubt. People tell me I shouldn't trust him, but I'm willing to give Simon the benefit of the doubt and wait and see what he actually offers.

It means that when you meet people, you will assume the best about them, until they give you reason enough to stop trusting them.

"1.A favorable judgement given in the absence of full evidence" if the available evidence is inconclusive and can not decide who is at fault/who is right then the benifit of doubt is applied Ex. I think you're stealing my money but Im going to give you the benefit of doubt.