major vs relative minor scales

The difference is in how the notes relate to their key notes. For example, C major and its relative minor, A minor, have the same notes but the notes of C major relate to C as the main note while those of A minor relate to A. It means all the notes will have a different quality, despite having the same pitch. The note B, for example, the 7th scale degree, is the so-called 'leading tone' of C major and resolves to it very naturally, a quality that's very often exploited when improvisiing using that scale. In A minor, B is the 2nd scale degree and doesn't have the same 'leading tone' quality that it does in C major.

The natural relative minor doesn't have a leading tone, so in composing or improvising, one is sometimes artificially created by raising the 7th degree (G to G#). But if you raised that same note, G, of the C major scale, you would be raising the important 5th scale degree and creating an "augmented 5th" with the key note C, which would give you a very different sound.
So the notes of both scales are the same but they all have a different quality when heard in relation to their respective key notes.

The minor scales give you a lot of flexibility. As Fretsource has said, in A harmonic minor, the relative minor to C Major, you have the G# leading note so you can use the E major chord (which doesn't exist in the key of C Major), and if you go into A melodic minor you have F# as well as G# in the ascending scale, allowing you to use Bm and D Major chords which wouldn't ordinarily fit. All good stuff.

A :-)

Major scale sound is happy, joy, dynamic
Relative Minor scale sounds are solemn, sad, mysterious, or ominous