A scale is the ratio between distance on the map and the distance it represents in real life. Put another way, the ratio of the scale tells you how many times smaller the map is compared to the real thing. For example, if a map has a scale of 1 to 50,000 (more properly written as 1:50,000) this means that one inch (1") say on the map itself, means that the distance is 50,000 inches on the ground (a bit less than a mile). Or with metric measurements, one centimetre on the map means 50,000 centimetres on the ground (500 meters or a little over 500 yards). It's easier to use metric lengths because all measures are multiples of 10. A reasonable ratio for the map to your state capital might be 1 to 100,000. On the other hand, the scale for a map (the plan) of your house might be 1:100. Incidentally, if you walk or cycle you may use a "one inch to a mile" map. On these, the each inch of the scale line or your ruler will represent one mile along the road or track. If you look in the key or legend you might find the unusual ratio of 1:63,360 because there are 63,360 inches in one mile.
Instead of ratios, mapmakers have made things easy for the map user. So you do not have to keep on doing the math to work out what distance the ratio means, most maps show the scale as a line. The line is marked with numbers showing what the distance is on the earth's surface. The line may show miles or kilometers, in tens, hundreds, or thousands, depending on the size of the map. Maps of a small area, like your street or town, will have a scale line in yards or miles (or the metric equivalent). Maps of bigger areas like those of your state may have a scale marked in tens of miles. In an atlas (a collection of maps), countries and continents may have scales of hundreds or even thousands of miles.
So the scale tells you about distance. From the ratio or the line, you can find out the distance. For example, you can see how far it is between two towns, or from one side of the country to another. Or you can tell how big something is, like a lake or mountain for example.
PROBLEM: In the map above the scale shows the island is 8 miles across. The ratio is about 1 to 300,000 (Since the line is about 2.125 inches long and represents 10 miles, so the line represents 633,360 inches, and so 1 inch on the map represents 633,360/2.125 = 298,051; or about 300,000. Check this calculation by measuring the screen to the 8 mile point and converting your measurement to miles. NOTE: Your screen must be set to a resolution of 1024x768 for the scale line to measure 2.125 inches.)