Interpretation of a limit in ergodic theory

Question

I have prove in a exercise that for a ergodic system $(X,\mathcal{B},\mu,T)$ if we take any integrable function $f$ with $\int_X f\,d\mu \neq 0$ then $$\lim_{N\to \infty} \log_N \left\vert \sum_{n=0}^{N-1}f \circ T^n (x) \right\vert = 1 $$

for $\mu$-a.e $x$.

What does this result mean?