What this saying, repeated by Benjamin Franklin, means is that it is easier to get people to do what you want by being nice than by being mean.
When Franklin uses the phrase "tart words" he means words that are angry. He says that if you use angry words when talking to people they will not want to be your friend.
Instead, he says, you have to use honey. When he says this, he mans that you have to use nice ("sweet") words and actions. If you act with a little kindness, it will be more effective than doing or saying many angry things (the gallon of vinegar).
In this saying, Franklin is using sour things as a metaphor for anger and sweet things as a metaphor for kindness and nice actions. He is saying that nice words and actions are more effective than angry ones.