Horse droppings are a basic ingredient for making manure.
You get them when your horse wakes up depending on the amount of food they ate the day before, unless they have a Ploutos' Parchment, which gives them equus instead. You can sell them for 3 equus each, or combine 600 of them with 200 straw in a workshop to make manure. They are also used in making the other two types of fertilizer. They cannot be bought in the store.