Answer: Major and minor can be used to refer to the greater and lesser versions of certain intervals (see question 48 on the difference between major and minor intervals) and you most often hear them used to describe the difference between music in a major key (music whose scale contains a major third upward from its "tonic," the starting note, so that the basic tonic chord is major) and music in a minor key (whose tonic chord is minor, since the scale on which it is based has a minor third from the starting note). The larger third that defines the major triad has a different emotional quality, it seems, from that of the smaller minor third that distinguishes the minor triad.

There are other differences between the major and minor scales, of course, but the main thing is that tonic chord to which the music returns home so often. "Home" in the first case is a cheerful optimistic lighthearted major triad, and in the other case is a tragic ominous forlorn minor (who knows how those feelings got started, but maybe there's something to them).