What is data mining and data mart for business intelligence?

Data Mining is the process of extracting knowledge that empowers decision making from the institution data (and other external data).

Business intelligence is one form of data mining, that is the statistical form (in most cases), the most important part of data mining that makes a difference in business intelligence is prediction, which is now know as Predictive Analytics. Without prediction, busuniss intelliegence is just Analytics. Which is the process to analyze data and extract important infromation that help the decision maker, then present this information in a very friendly and easy to digest visualization for top management.

A data mart is a local (usually small) data warehouse, which is a special kind of database that stores all of the institution's historical data in a non-transactional manner. Data stored in the data mart is used by Analytics and Predictive Analytics to provide their results.