People needed to know about how much a bushel was, and if they paid a certain amount of gold for a certain number of bushels, how much exactly were they getting. Gallons are related to the old-fashioned term bushel. When people want to trade things, they need to know about how much stuff they are getting. All of their measurements came from earlier Roman systems of measurement, and most of these came about because of merchants and trade.
A teaspoon is about the measurement of a dram, and was an unofficial measuring unit used by these apothecaries to represent one dram. They used pints, fluid ounces, drachms (drams), scruples, and minims.
Back then, they compounded the recipes in the pharmacy itself, so everyone needed the same recipe. Most of these measurements came from ancient apothecaries who needed measurements for their medicinal recipes.