Parallel keys and scales are keys and scales that share the same root. Understanding this concept is very useful to songwriters and for improvisation.
Many prominent songwriters employ parallel keys and/or parallel scales in their songs. The Beatles frequently used this device, in “While My Guitar Gently Weeps”, the verse is in the key of A minor and the bridge is in the key of A major. In “Penny Lane”, the verse is in B major and the bridge is in B major. Finally in “Norwegian Wood”, the verse is in D major and the bridge is in D minor.
You can also use parallel scales to great effect. An example I frequently teach students I,s parallel scales you can you to solo over a traditional dominant blues 12 bar progression. If, for example you're playing blues in the key of G, parallel scale options would be the G minor blues scale, G major blues scale, G mixolydian scale or G dorian scale. Those different scales offer a massive amount of varitey, especially if compounded (mixed together) creatively.
Lastly, another interesting trick you can use is to end a song on the parallel I chord of the key. So, if the song is in the key of A major you can end on some form of an A minor chord and if the song is in A minor, you can end on some form of A major.