Otoshi buta is a Japanese “drop lid” typically made from wood, although nowadays silicon, plastic, and other materials are also used. “Drop lid” means it is small enough so that it fits inside of a pan (not to cover a pan.) It is used to make simmered dishes mainly.
It has several different purposes. It helps to distribute heat evenly, enabling you to cook with a small amount of cooking liquid, and helps to save delicate vegetables (such as potatoes) and fish from falling apart by keeping them in the liquid. And flipping ingredients to give even flavor will not be required (this is especially helpful for delicate ingredients).
If you are using a wooden otoshi buta, you need to wet it in water first to prevent it from absorbing the cooking liquids of the dish. If you don’t have one, you can always make one using parchment paper or aluminum foil. Just cut a circle that fits inside of a pan, and make a small hole to let some steam out in the middle of circle.