How are the hands related to the mind? What is the deeper meaning?

All of the body is holistic and connected, and how much more so, the mind and soul are connected with the entire body. Hands represent actions or "doing". Symbolically, that's one of the reasons why the very first thing we do in the morning is to purify our hands, to demonstrate that all of our actions every day and all day, should be pure. Obviously one's hand motions, hand-shake etc. express (!) to a certain extent, what's going on in his mind and soul, nevertheless they don't limit him, and he can change them, just as he has free-will to destine his fate. Similarly, if you meant to ask about palm-reading, mainstream Judaism believes that one's Godly and God-given free-will is what's important, and that you shouldn't "lock yourself" into pre-determinism or fatalistic thinking or worrying by going to palm-readers or the like. Even if one was born with certain limitations of nature or upbringing, he can and should overcome them, and with the help of God and prayer, can overcome anything to be and do what he wants.