When referring to a two and three-dimensional plane, the x-axis refers to the horizontal width of a two or three-dimensional object. In the picture to the right you can see the x-axis plane going from left to right and intersecting with the y-axis and z-axis.
A good example of where the x-axis is used on a computer is on the mouse. By assigning a value to the x-axis, when the mouse is moved left to right increasing or decreasing the x-axis value will allow the computer to know where the mouse cursor is on the screen.
When referring to a two and three-dimensional plane, the x-axis refers to the