In a civil, intellectual argument, "granted" means that you accept some fact or principle--it is not in dispute.
A "grant" can mean a kind of gift. "Granted" means "I give you the debating point you want me to accept."
Imagine a debate between baseball fans on who was the best home run hitter in history.
"On the numbers, it has to be Barry Bonds. He hit more home runs, that's all there is to it. Period. End of story."
"I'm sorry, I can't agree. It was Babe Ruth. Granted, Barry Bonds hit more home runs, but his shouldn't count because he was on steroids."
He is saying "You say Barry Bonds hit more home runs. Yes. True. That's a fact. I acknowledge it. I give that to you. I grant it. Nevertheless, even accepting that, I don't concede the argument."