So, imagine you have a big box made out of dirt. Inside this box, you put a lot of poop from cows, pigs, or other animals. This poop is called manure, and it's good for plants to grow.
Now, you need to make sure this manure doesn't spill out of the box or get mixed in with the dirt around it. So, you build walls around this box using dirt, and make sure it's strong so it doesn't fall apart.
Once you have this box, you can store the manure inside it for a while, and then use it to fertilize your plants. But, you have to be careful when you go in or around the box because the manure can be smelly and not good for humans to breathe in too much.
Overall, an earthen manure storage is just a big box made out of dirt where you put animal poop to help grow plants.