One day I was sitting in the student union at the University of Utah when I noticed two students sitting near me working on a physics problem. One student was having trouble and the other was explaining how to do it using big hand motions. The first student nodded he understood. The second student left his friend to work on the problem on his own, and I watched him work for a while, then turn to his laptop, where he entered his answer into an online homework site and submitted it. This site gives you a little green checkmark when you get the right answer, and when the checkmark appeared, he pumped his fist. It seemed this little tutoring session went perfectly.
There was just one problem. The second student's explanation was completely wrong; he was literally 'handwaving'! So how was it, exactly, that the first student was able to solve the problem with such bad information? Beats me. What I can say is that tutoring is more than just the transfer of information from one mind to another. For a student, having the problem in mind, talking about it, getting feedback (even not so good feedback), thinking about it some more, and repeating the process as necessary, can produce remarkable results.
Of course a tutor should have a very good understanding of the topic. But they should also understand that that's not enough. One reason students may prefer a tutor to asking questions of their professors is they feel less intimidated. It's easier to ask questions and give tentative answers and just have a conversation. Whatever tutoring is, it should at least be that.