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Data Warehousing

Data warehousing combines data from multiple databases or data sources into a large database for the purpose of providing more extensive information retrieval and data analysis. Related data is summarized and correlated before it is presented to the user. Instead of having every piece of data presented, the user is given data in a more abridged form that best fits her needs.
Although this provides easier access and control, because the data warehouse is in one place, it also requires more stringent security. If an intruder were to get into the data warehouse, he could access all of the company’s information at once.

Data Mining

Data mining is the process of massaging the data held in the data warehouse into more useful information. Data-mining tools are used to find an association and correlation in data to produce metadata.
To use a simple analogy, it's finding the proverbial needle in the haystack. In this case, the needle is that single piece of intelligence your business needs and the haystack is the large data warehouse you've built up over a long period of time.
Data mining is also known as knowledge discovery in database (KDD), and is a combination of techniques to identify valid and useful patterns. These techniques include:

MetaData
Metadata provides context for data. It is used to facilitate the understanding, characteristics, and management usage of data.
Business Intelligence metadata
Business Intelligence is the process of analyzing large amounts of corporate data, usually stored in large databases such as a Data Warehouse, tracking business performance, detecting patterns and trends, and helping enterprise business users make better decisions.
Business Intelligence metadata can be used to understand how corporate financial reports reported to Wall Street are calculated, how the revenue, expense and profit are aggregated from individual sales transactions stored in the data warehouse. A good understanding of Business Intelligence metadata is required to solve complex problems such as compliance with corporate governance standards, such as Sarbanes Oxley (SOX) or Basel II.