Autocovariance and smoothness

I have just started to learn Time series from Shumway & Stoffer, 4th. My question is about the autocovariance. On page 25 there is something that I can’t understand it’s reason.

Very smooth series exhibit autocovariance functions that stay large even when the $$t$$ and $$s$$ are far apart, whereas choppy series tend to have autocovariance functions that are nearly zero for large separations.

Can anyone please explain the reason and intuition behind this statement?

Thanks.