The map scale is a fraction with a numerator of 1. The denominator shows how much length on the ground a unit of length on the map represents. On a 1:24,000 map, one cm on the map represents 24,000 cm on the ground. Since the scale is dimensionless, one of any unit represents 24,000 of the same unit on the ground.
Three standard paper map scales from USGS, showing the
Naval Academy in Annapolis. Printed on paper, each map is
approximately the same physical size, within about a factor of two.
This size reflects an easy size for printing presses to handle, and for
the user to manipulate.
They are referred to as quadrangle maps, because they are quasirectangles bounded by parallels and meridians. 




As a fraction, 1:24,000 is bigger than 1:250,000, so the 1:24,000 map is a larger scale map than the 1:250,000 map. As a corollary, the large scale map covers less area on the ground (unless it is physically much larger). The large scale map should have more detail.
The boundary between large scale and small scale changes with the context.
With digital data, the computer can change the scale for display, but the data was still collected at a specific scale which limits how much it can be blown up or reduced. Map scale and effective resolution.
With vector data, scale determines the number of points used to characterize a line segment and the spacing between the points. Large scale maps need many closely spaced points to accurately depict where a curved line goes. Small scale maps must be more generalized, and need fewer, more widely spaced points.
With raster data, scale determines the size of each pixel used to represent the data. Large scale data has many more smaller pixels.
Approximate conversions, degrees to metric.
Last revision 10/28/2017