what's to explain? looks pretty self contained and self explanitory to me. even if you were culturally unfamiliar with the gesture of nodding as an expression of aggreement, the statement pretty unambiguously implies its intention. furiously genericly implies passion or ardure or ferventness. so i don't see anything left to ambiguity nor requiring explanation. =^^= .../\...
Imagine if you nodded so furiously that your head fell off and rolled away. I dream that'll happen to me someday
The respective person is very upset at the same thing as his/her interlocutor. And is strongly in agreement on whatever measure the interlocutor proposes or words the interlocutor utters, which may be even a comment like 'annoying, isn't it?'
Furiously wouldn't mean upset in the context, it would mean vigorously. Vigorously shakes head. Complete agreement.