I have spent some time to proof the delta hedge error as described in this paper paper page 16-17 by Davis. The proof is discussed here Deriving Delta Hedge error in the B-S setup (part 2) (a post by myself)

I think the model is pretty complex (even the proof is tricky) and difficult to interpret. Where $Z$ is the hedge error, the main is this:

$$ Z_t = \int^t_o e^{r(t-s)} \frac{1}{2}\Gamma_s S_s^2(\sigma^2-\beta_s^2)ds $$ In words and plain English; how should this model be interpreted? (of course it can't be explained without equations but I am seeking intuition)

What does the realized volatility ($\beta_t) $actually mean in this context? For instance; if I have been daily delta hedging a short European Call position with maturity $T=2 year$ for a year ($t=1)$ then I can (the way I understand the model) evaluate my hedging error. But how does this help me in future? In various papers this result is presented to be a powerfull and strong result. The way I understand it: it just help me realize my hedge error in the past. I might have misunderstood it and there is more to it.