The song is for most part — albeit not entirely — written in C Major, but the scale he's playing is comprised of the tones C, D, E, F#, G, A and B. In other words, it is identical to the C Major scale except for that raised fourth — F# instead of F. Or otherwise put still, they are actually the tones making up for the scale of
G Major.
So when you play a G Major scale over a progression centered around a C root note, then that is Lydian mode. It has a kind of enigmatic tension to it, and likewise, each of the other modes adds a another type of tension to the music, which you cannot create by strictly adhering to the standard diatonic scale of the key you're playing in. This standard major scale itself is also a mode, i.e. Ionian mode.
Every major scale also always has a natural minor scale to go with it, which is comprised of the exact same tones, but the minor scale starts counting at a different point of the ladder, i.e. a minor third down from the root note of the corresponding major scale. By consequence, the C Major scale — or in modal terms, C in Ionian mode — has its counterpart in the natural A Minor scale, which in modal terms corresponds to A in Aeolian mode. Likewise, you can transpose this to other keys. If for instance you are playing in the key of G Major and you are playing the G Ionian scale — which is the standard G Major scale — then its natural minor counterpart would be E Minor, or in modal terms, E Aeolian. ;)
Another popular mode in progressive rock and jazz for instance is Dorian mode, which is a minor scale — it has a minor third — with a diminished seventh. When playing in C Dorian — i.e. the root note is a C — you would then be playing the tones C, D, D#, F, G, A, A#, or otherwise put, you are actually playing the tones of the A# Major scale. It shares C, D, F, G and A with the C Major scale, but the third is a D# instead of E (and thus: a minor third) and the seventh is an A# instead of B (and thus: a diminished seventh).
As a result of the third and the seventh both having been dropped by a half step in relation to the normal major scale (or Ionian mode), Dorian mode begets a somewhat medieval vibe. And that shouldn't be a surprise, because quite a lot of medieval music was composed in Dorian mode. Back in those days, musicians were not using the concept of major or minor scales and keys yet as we do today. They only knew the concept of modes, which owe their names to certain regions in Greece where the individual modes were popular. So instead of saying
"This is a song in D Minor (or F Major)", they would say
"This is a song in D Aeolian (or F Ionian)." Or at least, that is to say, sort of, because that's not exactly correct either. ;)
You see, the alphabetic naming of tones is something that only appeared much later. Instead, people in the middle ages were using different names for the tones, i.e. (for the tones comprising the C Major scale) do, re, mi, fa, so (or "sol"), la and ti (or "si"). Over here on the European mainland, we still use those names for the individual tones, and we use the alphabetic designations for chords. So we talk of the C chord, which is comprised of the tones do, mi and so(l). ;)
Explaining music theory isn't really the scope of this thread — although on the other hand, I don't really see why not ;) — so I'll just defer those interested in the subject toward
the Wonkypedia article. :p
