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. Two important concepts in descriptive statistics are:
Inferential statistics, as the name indicates, are used to make inferences or predictions based on a set of data that is assumed to have been sampled from a population of interest. For example, when we sample, say, 1,000 people to determine whom they intend to vote for, we're not interested so much in those 1,000 people as we are in what those results mean in regard to the voting preferences of the population as a whole. Two main areas of inferential statistics are parameter estimation, where sample data are used to estimate the parameters of a distribution (for example, a normal distribution), and hypothesis testing, where sample data are used to make claims or answer questions regarding the population as a whole.
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.