The AMG button just sounds like it turns everything off, traction control, loosens suspension but Hammond did not make it very clear. :\
No I think what it is, is a macro key basically, hence him emphasising 'how YOU want it'.
I think it just remembers all your favourite settings from the other options and allows you to engage them via one button rather than spending 5 minutes doing it all one by one every time.
No idea what the waffle about 'it puts it through a special.... thing' was though :/