The harmonic minor scale contains the same notes as the natural minor scale, but with one important alteration: the 7th degree of the scale is raised one half step: instead of a ♭7, the harmonic minor has a major 7.

Here is the A harmonic minor scale:

R 2 ♭3 4 5 ♭6 7 R
A B C D E F G# A

In classical music the harmonic minor is played ascending but when descending the 7th is flatted. In jazz that rule is ignored. This scale is common in progressive rock because that style is very classical based. But it is also very common in Latin styles and jazz.

Raising the 7th gives us a strong resolution to the root note. In other words, it gives us the ti to do as in the major scale, so it is very satisfying when we get back to the root note.

But it also creates an augmented 2nd (1½ steps) between the ♭6 and the 7th degree of the scale. Since the augmented 2nd is a very difficult interval to sing the melodic minor scale is often used.

Here is the G Harmonic Minor Scale on Guitar:

The Harmonic Minor Scale on Guitar