Satriani
Ok, this is reallllllly realllllly simple. Just sounds fancy. What happens when you use a 'pitch axis' is that you are centering around ONE key. Lets takes a simple example...
If we're in say the key of E Major, what is the Root or Tonic? It's E of course. Now you play a couple of bars in E Major, while the bass is playing in E, and then you suddenly switch to ANY other scale in the key of E. So you could switch to E Natural Minor, while the AXIS is still E. A good example of pitch axis is Joe Satriani's Always with you, Always with me. The song is in the Key of B Major, but for the 'solo' section, he switches to B Minor for his scale choice, but the Key is still in B. Therefore, he has not changed KEYS, but rather scales within the Key of choice.
There's really not much more to say about pitch axis. It's that simple ?