The horizontal axis is also called the x-axis as, on a graph the x values are plotted along this line. It is the line representing the "independent" variable which is the value that is NOT dependent on the second value.
For example, when driving a car, the distance covered is dependent upon the speed of the vehicle. So in this instance, the speed would be the independent variable. Similarly, in Economics, if a quantity demanded increases (horizontal axis), so too does the price usually increase (vertical or y-axis). Time is also often plotted this way. As the length of time increases, so too does the amount saved (for example). Depending on the information required, this can obviously change.
The axes allow information to be measured against other information so that conclusions can be drawn.