Here's why it makes sense:
* Familiarity: The back of your hand is something you see and touch constantly. You know its contours, the lines on it, and its overall shape intimately.
* Knowledge: The phrase implies a level of knowledge and familiarity that is so deep, it's as if you know the subject "like the back of your hand."
Similar Phrases:
* "Know something like the back of your hand"
* "Know something inside and out"
* "Be familiar with something like the back of your hand"
These all point to the same core idea: a deep level of understanding and familiarity.