Data, by itself, is a collection of recorded information. In an unprocessed, non-analyzed state, it's relatively useless. It might have potential, and only has that if the data is stored in an effective fashion (the "garbage in, garbage out" analogy applies here.) Data mining is one method for making more use out of data. It has applications in many industries, but is most commonly discussed in terms of business use for consumer and market forecasting.
Edelstein describes data mining as "[using] sophisticated statistical analysis and modeling techniques to uncover patterns and relationships hidden in organizational databases -- patterns that ordinary methods might miss." [1] Data mining is part of a larger area of research known as "knowledge discovery." Many organizations maintain large databases filled with transactional data. Some buy "warehouses" of consumer data that can be "mined" for new information. This is where the term is likely derived from.
Data mining is a methodology and tool for business. It does not replace the need for comprehending statistics or understanding one's business [2]. That is, it's not a "magic solution". Like any tool, if it's misused or not fully understand, data mining can yield faulty or misleading results.