Map Scale
A map is a representation of a part of the world that is presented at a convenient scale to fit on a piece of paper of a suitable size to be conveniently usable by the map reader. Say for example to fit a map of Tasmania onto an A2 sheet of paper you would probably use a scale of about 1:1,000,000.

Image of 1:100,000 Scale Bar
Source: http://rsteward.napsk12.org/map-skills
What does it mean?
So what does a scale of 1:1,000,000 mean, and why use this scale over say 1:1,123,986?
A scale of 1:1,000,000 is a simple ratio (or fraction), which means that one unit on the map represents 1 million units on the ground. In other words 1 centimetre measured on the map represents 1 million centimetres, or 10 kilometres, on the ground.

Australian Population Distribution in 2000, Source: http://sgrhs.unisa.edu.au/student/prep_rural_prac/1-major_issues.htm
To answer the second question about the preference of scales such as 1:1,000,000 over 1:1,123,986 is a matter of convenience for the map user. It is far easier for the map user to measure a distance on map at 1:1,000,000 and convert it to a real world distance than at an ‘odd’ scale. However if the measurement of distance is not considered important for the map purpose (for example a map showing the relative populations of major cities in Australia), then it is quite acceptable to use an odd scale for the reason that it fits better in the space provided (such as at the bottom of a page in a report on population growth).
Scale and GIS
When data is captured digitally for use in Geographic Information Systems (GIS) it is captured at a scale (or maximum resolution). This means that the information is designed to be displayed at a maximum resolution. If the viewer zooms in to view the “map” at a greater resolution then the accuracy of the positional data can’t be guaranteed. There is quite often a misunderstanding among inexperienced GIS users that because the information is in the computer, you can keep zooming in almost indefinitely.
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