Intuitive example of The Renewal Reward Theorem with Markov Chains.

Question

So I'm trying to study som Markov Chains. And I've stumbled across "The Renewal Reward Theorem" or "The elementary renewal theorem", it seems to have different names. The theorem basically says:

$lim_{t\to \infty} \frac{1}{t} m(t) = \frac{1}{E(S_1)}$

I'm trying to find a intuitive way to understand this. $m(t)$ can be interpreted as "# customers that came to the store during time $t$". And $\frac{1}{t} m(t)$ to be like "Every time $t$ so many peoples arrive". But I don't know what to think if the right and side and limit of the expression.

Thanks if you can give a nice simple example of this :)