The Harvest Sprites are tiny elves that live in the cave connected to the carpenters' clearing. They are unique in that they all share the same affection value (i.e. you only need to talk to/gift one of them and they all have the benefits; multiple talks/gifts have no benefit). If you get them to high enough affection they will feed your animals on days you forget or aren't able to (sick, typhoons, weddings, certain cut-scenes). They also play an important part in restoring the Vineyard and getting a Power Berry from Stu.
When the player first meets them, the Sprites speak in Pig-Latin. Giving them gifts will help them speak normally. The main Harvest Sprite is always found in the main cave, while the other two live in their little cave (the hole in the wall in the cave). If you go into their cove, you will notice another small hole which (apparently) connects to your barn (and explains how they are able to feed your animals during typhoons).
If you get a high enough affection with the sprites the two deeper in the cave will reveal their names: Arthur and Billy. The main sprite is Carlos. An interesting note is that Arthur and Billy both will appreciate Rare Metal and Moonlight Stone as gifts, while the Carlos doesn't care about those. Arthur is (apparently) a good cook, while Billy is not.