One of the three types of minor scales. This scale (along with the harmonic minor scale is used heavily by heavy metal guitarists such as Yngwie Malmsteen.

To form the scale, we use the Harmonic Minor and simply raise the 6th degree 1/2 step. C harmonic minor:

C D Eb F G Ab B C |___|___|____|___|___|____|___| 1 1/2 1 1 1/2 1.5 1/2

The numbers between the notes denote the interval between them. Now, to derive our melodic minor, we simply raise the VI degree of the harmonic minor scale (Ab -> A). Here we have it:

C D Eb F G A B C |___|___|____|___|___|___|___| 1 1/2 1 1 1 1 1/2

A note on improvisation: Historically, this scale has been played the way it is written above only while ascending the scale. This is because of a tendency in classical music to make runs up and down the scales to define tonality. However, if you come back down the melodic minor scale, it starts to sound like a Major scale. Since we want the minor tonality defined right away, classical musicians played the natural minor scale descending in the melodic minor scale. However, since most of its usage in rock has little to do with classical music, this convention has become a bit obsolete. If you plan to use this scale to improvise in rock (hey, why not), I suggest you play the same scale up and down. If you're a classical nut, don't let me stop you from playing the Aeolian down. After all, it's your ]]life.
Basically, the scale is used over any kind of minor chord to solo.

If you're familiar with II-V-I progressions, you can use your knowledge to create new ones using the harmonic minor scale as the base scale. Simply slap in your notes, and form the chords on top of that.