Playing "outside" is the concept of playing notes not specifically in a harmony. In a diatonic progression, all the chords are "harmonized" to fit the scale of the tonic. If A minor is the I chord, all the changes should be chords with notes in A minor. Playing "outside" increases the tension, and makes things sound more "jazzy."
There is a spectrum of how "out" you can get. You can play a scale over a chord that has NO notes in the tonic scale. That is the most "outside" you can play.
The simplest way to do this is to play a minor pentatonic (the blues scale) either a half-step above or below your tonic. With the example of A minor, if you start your minor pentatonic blues scale on Bb or Ab, you will be playing ZERO notes in A minor. That's as outside as you can get. Same with a tritone -- or augmented 4.
You can also play scales that are "less" outside with scales that have some key notes in the tonic scale and some notes out. Play a minor pentatonic starting on the fifth and or ninth.
The minor pentatonic is a scale most guitarists learn early on -- this is a way to use that scale to get some very interesting sounds.
Here's some other lessons from that same guy.