A "good handshake" means having a firm and confident grip when you shake someone's hand. It shows respect, friendliness, and trustworthiness. Full definition
A good handshake is firm and dry, lasts two or three seconds and is accompanied by eye contact and a smile. (entrepreneur.com)
Your father probably discussed with you the importance of having a good handshake, but did you know that handshakes really are a big determining factor when it comes to first impressions? (entrepreneur.com)