Hand dipped means they scoop real ice cream out of a tube, and use a milkshake mixer to blend it together with some milk and flavorings. It is the 'old school' way of doing a milkshake.

Now - most fast food places just get milkshake mix and pout it into a milkshake machine and just draw out milkshake mix that has been frozen to the right consistency.

Hand dipped allows you to use other ice cream flavors and vary the richness of it by using more or less milk.