Наговорились как мёду напились - what does it mean?

it means that a good converstaion is sweet like honey.

This saying dates back to the old times of the ancient Rus’, when there were no strong alcoholic drinks such as vodka. But for holidays or feasts people used to make some low alcohol liquors based on honey. Honey actually improves the immune system very much, so those liquors vere not only tasty but also healthy.
Therefore, the saying compares a hearty conversation with drinking honey liquor, as it brings the same pleasure, relief and health profit.

Yea, the saying is all about a good conversation being similar to a light and sweet hop. By the way, we still drink “honey” - for pleasure or as a medicine. It’s actually called “nastoyka” (настойка) or “nalivka” (наливка).