Sheep have been in Minecraft since the beginning, being your method of gathering wool to craft a bed and sleep through the night. This is a much faster and safer way of gathering wool as opposed to collecting string from spiders. If you are looking to breed sheep or keep them alive, here is what they eat in Minecraft.
While you may see sheep lower themselves to the ground and eat the grass on top of dirt blocks, you can not feed them grass yourself. Instead, you will need to either gather or grow Wheat and use that to feed them to refill their health or have them breed. Wheat can be found in gardens in villages, or you can grow it by getting seeds from breaking tall grass and planting them on tilled soil from a hoe. Place water blocks nearby to have it grow faster.
When you have the Wheat in hand, any nearby sheep will follow you unless you put it away or get far enough away from them. Interact with them, and they will eat the Wheat. If hearts start flying from them, they are ready to breed and will search for another sheep doing the same thing to make a baby sheep. If you feed Wheat to a baby sheep, it will grow to adulthood faster.