Seventh chords are most easily thought of as an extension of triads, and our labeling system reflects this. In the same that we create a triad by inserting a 3rd into a 5th, we create a seventh chord by adding a 3rd on top of a triad. They are called seventh chords becuase this new note creates an interval of a 7th between the chordal root and the new pitch.
Because they are stacked thirds, seventh chords are still considered tertian harmony. They are prevalent in almost all styles of Western music, and we have developed many systems to describe how they function harmonically. Again though, we must first be able to classify and label them in an structural manner that does not rely on key-based functions. We name the chord members by the distance above the bottom pitch when the chord is stacked in thirds:
All seventh chords have exactly four notes, although certain chord members can occasionally be omitted (and therefore implied) depending on the context. With four pitches, there are four possible configurations that depend on which note of the triad is in the lowest voice. Like triads, we call these inversions, and we use the same shorthand system to label inversions that we used with triads.