Polyphonic music is made up of two or more independent melodic voices. This is different from a monophony, which has only one voice or melody, and a homophony, which is one voice accompanied by chords. Polyphonic music was popular in the late Middle Ages and Renaissance, and used commonly by the Catholic Church.
Here are two examples of polyphonic church music. The one on the right was written by William Byrd, an Elizabethan composer (see bookmark for page 134).