A chord plays, you name its quality. Being able to tell a minor 7th from a dominant 7th by ear changes how fast you learn songs, write progressions and arrange.
Level 1 is major or minor only. Level 2 adds diminished and augmented, level 3 the sus2 and sus4 chords, level 4 the major and minor 7ths and 6ths, and level 5 the dominant 7th, half-diminished and diminished 7th. Levels 6 and up add add9 and the 9th chords, whose colors are much closer to each other.
Listen to the middle note of the chord. In a major chord it sits a major third above the root and sounds open; in a minor chord it sits a semitone lower and the whole chord darkens. Comparing the two back to back on the same root is the quickest way to lock it in.
Because they share three notes with a triad you already know. You're listening for the one added note and how it colors the chord, which takes more focused listening than the big contrast between major and minor.