In the olden days, it originated as a gesture of peace by demonstrating that the hand holds no weapon.
These days, to me, it’s more of an indication of character. Limp handshake? Wish-washy and questionable moral center. Iron grip that hangs on too long? Trying too hard. (Check to see if you still have your wallet.)
Fair or not, this is always my initial judgment of someone. Next time on “Things People Probably Don’t Care About Any More”, eye contact. How much is too much?