Why is $dS/S$ an estimate of realized volatility?

For one period, $dS/S$ is an estimate of realized volatility, which we can annualize by dividing with $\sqrt{\Delta t}$.

But.... why? How is $dS/S$ an estimate of volatility? Volatility is, to me, how big the random fluctuations are. But if I have a stock price that goes 100, 110, 120, 130, 140, 150, 160, every day, then that's not a random fluctuation, and the volatility is 0 .... yet, using above formula we get that the volatility is 0.1 for the first day.