Consider two points $a$ and $b$ and ray traveling between these two points. Now imagine two nearby paths $p({\bf x})$ and $p({\bf x}) + \epsilon q({\bf x})$, connecting those points. Here $\epsilon$ indicates a small number and $q(x)$ is an arbitrary (well behaved) function. Clearly the traversing time for a ray depends on the path $t = t(p)$
The version above just indicates that
$$
t(p) \approx t(p + \epsilon q)
$$
Or in other words
$$
\lim_{\epsilon \to 0}\frac{t(p) - t(p + \epsilon q)}{\epsilon} = 0 = \int_a^b \frac{\delta t}{\delta p}q ~{\rm d}x = \delta \int_a^b t(p){\rm d}x
$$
where I used the functional derivative $\delta$ in the last step. The last equation is just the variational formulation of the principle