When most people heat the word "cylinder" they are thinking of a "right circular cylinder" -- that is -- a circle which is copied up and down along a line perpendicular to the plane that circle lies in.
The term "cylinder" can more generally refer to a curve copied along any line. So for example,
$y=x^2$ is a parabola in the plane, but since there is no reference to $z$, the parabola $y=x^2$ and $z=5$ also satisfies this equation (same for $z=$any constant). So in 3-space, the graph of $y=x^2$ is a parabola copied up and down the $z$-axis. Instead of a circular (regular old) cylinder, you have a "parabolic cylinder".
If you notice, all of the equations you have listed above only list 2 out of the 3 variables (x,y,z). So the graphs of these surfaces are graphs of a curve copied along the remain variable's axis.
For example: Here is (part of) the graph of $z^2=y$ (another parabolic cylinder)...
Notice that the parabola $z^2=y$ (in the $yz$-plane) has been copied along the $x$-axis.
Wikipedia Page on Cylinders -- see "other types of cylinders"