The mode is the frequently occurring number in a set. The mode of these numbers:
5, 5, 10, 10, 10, 10, 10, 10, 20, 100
whereas their arithmetic mean is 17.3.
The mode is the peak of the probability distribution, and what it tells you is a typical value. For example, when looking at incomes, the mode of incomes tells you the income of the typical person: the mean can be raised by a small number of people with very high incomes, while the mode is unaffected. It shares this property with the median, but differs in that it gives you a typical value, rather than a half way value: of course they are sometimes identical and often close.
The mode is also what you are most likely to think of as the average when looking at a graph: the peak is far easier to pick out by eye than the point at which the area under the curve each side is equal (the median) or the mean: unless a probability distribution is symetrical, like the normal distribution.