A hymn tune is the melody of a musical composition to which a hymn text is sung. Musically speaking, a hymn is generally understood to have four-part (or more) harmony, a fast harmonic rhythm (chords change frequently), with or without refrain or chorus.
From the late sixteenth century in England and Scotland, when most people were not musically literate and learned melodies by rote, it was a common practice to sing a new text to a hymn tune the singers already knew which had a suitable meter and character.
There are many hymn tunes which might fit a particular hymn: a hymn in Long Metre might be sung to any hymn tune in Long Metre, but the tunes might be as different as those tunes that have been used for centuries with hymns such as Te lucis ante terminum, on one hand, and an arrangement of the calypso tune used with Jamaica Farewell, on the other.