Proper in this instance means the main body of the hand, the part that has no other identifier. the fingers and wrist have other terms to identify them, the hand proper does not. If I say the the hand you are not sure whether I mean the hand as a whole or that part in particular so it is called the hand proper. Its an old usage of the word, but that is common in anatomy text.
From webster it is the 6th definition. Proper: strictly limited to a specified thing, place, or idea