Definition:Axis/Z-Axis

Definition
In a cartesian coordinate system, the $z$-axis is the axis passing through $x = 0, y = 0$ which is perpendicular to both the $x$-axis and the $y$-axis.

It consists of all the points in the real vector space in question (usually $\R^3$) at which all the elements of its coordinates but $z$ are zero.

As the visual field is effectively two-dimensional, it is not possible to depict a three-dimensional space on a visual presentation (paper, screen and so on) directly.

Therefore the representation of the third axis of such a cartesian coordinate system is necessarily a compromise.

However, if we consider the plane of the visual field as being a representation of the $x$-$y$ plane the $z$-axis can be imagined as coming "out of the page".

Also see

 * Definition:X-Axis
 * Definition:Y-Axis