So I'm reading that you already understand the grades as weda has posted them.
Now how would higher grades correspond to fitness and experience?
Skills != grade != fitness. Grade is equal to difficulty and is subjective so this type of comparison never works. Some explanation on why this doesn't work in
How does a route setter grade a climb?
and Rating unorthodox climbs
Could it be compared with scrambling or rock climbing grades?
I can't find any official source but reading the descriptions I'd say they are equal to the scrambling grades commonly used. So I would suggest they would sit thus:
A : Walking (not graded)
B : Grade I scramble
C : Grade II scramble
D : Grade III scramble
E : Moderate/Difficult climb Sport grade I or II
So only grade
E would be on any climbing scale.
Disclaimer: I made this comparison up based on the descriptions on wikipedia. They seem to match the scrambling grade descriptiions. I've never been on a via ferrata!