In general a plane in $\mathbb{R}$^3 is given by an equation of the form $ ax + by + cz = d.$
If for example $a= 0$ you see that the equation is "independent" of $x$. So that means that given a point in the plane, you can vary $x$ as you like and still move in the plane. Or said differently, if you travel parallel to the $yz$-plane, you stay in the plane. So the plane is normal (perpendicular) to the $x$-axis.
Likewise if $b = 0$ the plane is normal to the $y$-axis.
And if $c = 0$ the plane is normal to the $z$-axis.