Most hospitals have an area called a morgue, where dead bodies are stored until they are buried or cremated.
After a person dies, that person's body is often placed in a morgue until it can be transported to a funeral home, church, or temple for a memorial service or funeral. Occasionally, a body needs to be identified by relatives, and that often happens in a morgue as well. Another word for morgue is mortuary. The word comes from the French La Morgue, which was one specific building in 1800s Paris. It replaced the much more blunt term "dead house."