It is minor because it is the smaller of the two sevenths, spanning ten semitones.
For example, the interval from A3 to G4 is a minor seventh, as the note G4 lies ten semitones above A3, and there are seven staff positions from A3 to G4.
A well-known example, in part due to its frequent use in theory classes, is found between the first two words of the phrase "There's a place for us" in the song "Somewhere" in West Side Story.
[4] The most common occurrence of the minor seventh is built on the root of the prevailing key's dominant triad, producing the all-important dominant seventh chord.
During the common practice period the minor seventh was prescribed as a dissonance, requiring resolution to a consonance.