When you hear the word parody, you may think of a satirical treatment of serious material. That doesn’t seem like the kind of thing one might hear in a church.
But in the case of a parody mass, it’s ok (most of the time—I’ll tell you about the exception in a bit). A parody mass is one which uses a secular song as the musical theme for the setting of the words of the mass. It has nothing to do with a satirical parody. It was a technique that was widely used in the 16th century. It is sometimes called an imitation mass.
Some of the more well-known parody masses are the Westron Wynde masses of John Taverner, Christopher Tye, and John Sheppard, and masses based on the tune L’homme armé, some of the most well known being the settings by Josquin Des Pres, Johannes Ockeghem, and Guillaume Dufay. You can see an article on L’homme armé, called the “most borrowed tune ever” here.
Of course one should probably be selective in one’s choices for mass themes.
Orlando di Lasso (Orlande de Lassus) wrote a mass now known as the Missa Entre vous filles. Here’s the problem. In the song Entre vous filles de quinze ans (written by Jacobus Clemens non Papa), fifteen-year-old girls are advised not to go to the fountains because they are distracting. Clemens non Papa is rather specific about what is distracting about them. You can imagine that some people were not too happy when they found out where the mass theme came from.
The use of the parody mass dwindled, but the musical intermingling of sacred and secular has continued. Martin Luther used folk tunes for chorales. Classical themes have been used for hymn tunes and given new words.
Jan van Eyck (circa 1390–1441) [Public domain], via Wikimedia Commons, https://commons.wikimedia.org/wiki/File%3AJan_van_Eyck_-_The_Ghent_Altarpiece_-_Singing_Angels_(detail)_-_WGA07642.jpg