Data Warehouse: (An Oracle Docs Definition)
A data warehouse is a relational database that is designed for query and analysis rather than for transaction processing. It usually contains historical data derived from transaction data, but can include data from other sources. Data warehouses separate analysis workload from transaction workload and enable an organization to consolidate data from several sources.
Data Mart: (An Oracle Docs Definition)
A data warehouse that is designed for a particular line of business, such as sales, marketing, or finance. In a dependent data mart, the data can be derived from an enterprise-wide data warehouse. In an independent data mart, data can be collected directly from sources. Is the categorization of your datawarehouse data to a particular line of your business. For example BIG DATAWAREHOUSE DATA becomes PURCHASING DATA and SALES DATA and INVENTORY DATA. So a Data Mart is, loosely speaking, a piece of the big thing.
Data Mining: (An Oracle Docs Definition)
Too much data and not enough information — this is a problem facing many businesses and industries. Most businesses have an enormous amount of data, with a great deal of information hiding within it, but "hiding" is usually exactly what it is doing: So much data exists that it overwhelms traditional methods of data analysis.
Data mining provides a way to get at the information buried in the data. Data mining creates models to find hidden patterns in large, complex collections of data, patterns that sometimes elude traditional statistical approaches to analysis because of the large number of attributes, the complexity of patterns, or the difficulty in performing the analysis.
OLAP: (An Oracle Docs Definition)
OLAP functionality is characterized by dynamic, multidimensional analysis of historical data, which supports activities such as the following:
Calculating across dimensions and through hierarchies
Drilling up and down through hierarchies
Rotating to change the dimensional orientation
OLAP tools can run against a multidimensional database or interact directly with a relational database.
Oracle® Database Data Warehousing Guide 10g Release 2 (10.2)
Oracle® Data Mining Concepts 10g Release 2 (10.2)