we mean that the chord has a major 3rd with respect to the name of the chord and that the chord is of the type 1 3 5
For example
C major chord is
C E G
C minor chord is
C Eb G
It is called minor because the 3rd is minor, a semitone smaller
Other intervals can be major or minor. For example the interval of 6th, 7th 9th with respect to bass etc.
Their name comes from the major scale.
For example the interval C B is called interval of major 7th since B natural is the 7th note of the C major scale.
C Bb is called interval of minor 7th because it is smaller one semitone.
So the chord C E G B (Beathe - Pink Floyd at the lyrics point "for lomg you live and high you fly..." is called C major 3rd major 7th but for reasons of word economy we may call it C major 7th.
Further reading:
Harmony - Piston
Bach bass rules - Bach, Niedt
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