To mummify is to make a mummy — to prepare a dead body for preservation after burial. Ancient Egyptians would often mummify bodies by wrapping them in cloth. Don't try that at home!
Many cultures have had a tradition of mummification — in other words, they would mummify their dead, often to insure a happy afterlife, by removing the internal organs, treating the body with minerals and oils, and wrapping it. Sometimes burial conditions, like a very dry location, have served to accidentally mummify a body. Mummify adds the verb-forming suffix fy to mummy, rooted in the Arabic mumiyah.