When the beat divides into two parts, it is called a simple division of the beat. Simple divisions often have a quarter note for the beat, making the the division of the beat two eighth notes. If the half-note is used as the beat, then the quarter note would be the division of the beat.
Time signatures of simple division meters
As presented in the ‘Time Signature and Meter I’ lesson, the top number of a time signaure states the number of beats, and the bottom number of the time signature states the value of the beat. In simple meters, this is straight forward.
The song "Oh When the Saints" looked at above has simple division of the beat and can be notated with a quarter note as the beat.
When the beat divides into three parts, it is called a compound division of the beat.