What is the difference between there major scale and the aeolian scale?

To understand the difference between these two common scales, we need to think about where all scales come from in the first place. The typical major scale, containing seven notes is where all scales will begin. 

A 'major' scale is this scale played in its most simple form from the root note (or 'tonic') up seven notes to the note an octave above this note. It is characterised by its major 3rd and major 6th and major 7th intervals which give it its 'happy' sound. A famous song that uses this scale is (to pick from many examples!) 'Someone Like You' by Adele.

The minor scale or 'aeolian' is a variation of this scale. Instead of starting on the tonic note, we start our scale from the 6th note. Here, the relationship to all the other notes in the scale gives us a completely different set of intervals. This is characterised by minor 3rd, minor 6th and minor 7th. This gives the music a much sadder, angrier and overall moodier vibe. The 7th note of the scale can be raised a semitone to form the hormonic minor scale. A famous song that uses this scale is 'Paint it Black' by the Rolling Stones.