I recently reached level 2 farming (yes, I'm new). I have noticed that the farmers are watering the plot as it matures, but I have not noticed that it has made any difference in the speed at which the crops appear to grow or if watering the plot makes any difference at all. Are there advantages to watering the garden while waiting for new crops to grow or should these farmers do something else while I wait?

It depends upon your personal preference and the skill that your farmers already have. Farmers gain skill when engaged in any farming activity, including watering the crops. Master farmers are an important asset to the game, so letting them water the crops is not a waste of time. However, if you have a problem with food now and need to get to Level 3 of Farming quickly, putting your farmers to work at the research table can be a good move. Also, if your farmers are already masters, then they don't need to build their skills by watering crops and can be safely used elsewhere when the farm is empty.

Also, if you're short on food and your berry bush is still in decent shape, you can always plunk the farmers on the bush during the growing season. ^^