A parody mass is a musical setting of the mass that uses melodies from other musical works. This kind of mass was popular in the 16th century. "Parody" in this sense does not mean "parody" in the modern meaning of the word. It is not about poking fun at something. A parody mass is one that borrows musical material. The music might be borrowed from a chanson or motet, usually one by another composer. At that time there was nothing shameful about using other composer's tunes. Today it would be called plagiarism (stealing other people's ideas).
The parody mass was very popular during the Renaissance: Palestrina wrote about 50 parody masses. Some examples of early parody masses include the Missa Malheur me bat, Missa Mater Patris, and Missa Fortuna desperata by Josquin Desprez. By the middle of the 16th century, a large number of masses composed used the parody technique.