capacitance - Physical explanation for capacitive circuit

In capacitive circuit, the voltage and current are out of phase. the current leads the voltage by 90 degrees. this can be explained by these two equations:

$$V = V_{\max} \sin \omega t$$

$$I = I_{\max} \cos \omega t.$$

Now, my question is that what does this statement mean physically that "current leads the voltage by 90 degrees? It is clear mathematically that if $V = 0$ then $I$ is maximum but how do we explain this physically? hope you understood my question