When you scale something, you adjust the total size or amount but maintain the original proportions or relative sizes or amounts of the components. Think of "scale" in the sense of a ruler divided into certain units.
One way to think of it is changing the unit of measurement without changing the values. A map, for example, might have a notation like 1" = 1 mile (in the US, anyway), meaning units of inches on the map are equivalent to units of miles in real life. You change the overall size or amount just by changing the units you measure with. Another example of scaling would be a recipe, where you want to make a lesser or greater total amount of something and need to keep the ingredients in the same proportion.
If you keep the unit of measurement the same when you scale, you adjust the values so they are in proportion. Use the recipe analogy. In volume measurement, 4 cups equals one quart. Say a recipe calls for 1 quart of X and 4 quarts of Y, and you want to make 1/4 as much. You could change the unit of measure from quart to cup, making it 1 cup of X and 4 cups of Y. Or, you could keep quarts as the unit of measure and adjust the values to 1/4 quart of X and 1 quart of Y.
The second alternative would be scaling the values (or numbers), between 0 and 1. When you scale numbers to fit in a certain range, you pick a value that is within the range for the largest example, and then make the other values proportional to their original relative size.