The word "statistics" can be used both to describe numerical data and to describe the methods used to deal with that data. The aim of statistics to provide useful information via mathematical operations on numeric data and includes collecting, analyzing, and presenting that data.
Statistics are used in many fields. Many have encountered their use in politics or sports. More involved uses of statistics can be found in many fields, from medicine to the social sciences to engineering.
Statistics can be classified as descriptive or inferential statistics. Descriptive statistics, as the name indicates, are used to describe data. Inferential statistics, as the name indicates, are used to make inferences or predictions.
One important concept in descriptive statistics is that of measures of central tendency, which aim to summarize data through a single value that represents the "middle of the road" in some way or another. Another important concept is that of measures of spread or variation, which aim to summarize how far the data are spread out.
See also normal distribution and hypothesis testing.
See also "The Force of Statistics" by Stephen Leacock.
You may also be interested in reading about Interesting Statistics (page 1), (page 2) on our sister site, All Fun and Games.