Business Intelligence, Knowledge discovery in databases (KDD) and Data mining: Definitions
Kmining.com

Business Intelligence (BI) - Set of numerous techniques, methods and tools for gathering right data and turning it into knowledge and competitive wisdom. (Definition by Kmining.com)

Knowledge discovery in databases (KDD)
- is the (iterative and interactive) nontrivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. [Fayyad96]

Data mining
- the step in the process of knowledge discovery in databases, that inputs predominantly cleaned, transformed data, searches the data using algorithms, and outputs patterns and relationships to the interpretation/evaluation step of the whole knowledge discovery in databases process. [Fayyad96]
- The science of extracting useful information from large data sets or databases. [Mannila01]
- Data mining is a new discipline lying at the interface of statistics, database technology, pattern recognition, machine learning, and other areas. It is concerned with the secondary analysis of large databases in order to find previously unsuspected relationships which are of interest or value to the database owners. [Hand98]
("secondary" means that the data is being analysed after it has been collected for other "primary" reason, for example saved transactions for billing etc.)
- is the exploration and analysis, by automatic and semi-automatic means, of large quantities of data in order to discover meaningful patterns and rules [Berry97]

As you can see there are a lot of different definitions available and even sometimes KDD (Knowledge Discovery in Databases) and data mining are thought to be synonyms. Actually it all depends how you look at them or what do you emphasize - probably the easiest way to think about them would be that KDD is the whole process of discovering and data mining is the intelligent technical step in that process.

Then again, there are some process models for data mining and they include also different steps from KDD. No need to be confused - as said before, everything depends how do you look at things and what you emphasize.

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[Fayyad96] Usama M. Fayyad, Gregory Piatetsky-Shapiro, Padhraic Smyth: From Data Mining to Knowledge Discovery: An Overview. Advances in Knowledge Discovery and Data Mining, 1996: 1-34
[Mannila01] David Hand, Heikki Mannila, and Padhraic Smyth: Principles of Data Mining. MIT Press, Cambridge, MA, 2001
[Hand98] David Hand: Data Mining: Statistics and More? The American Statistician, Vol 52, 1998: 112–118
[Berry97] J.A. Berry, G. Linoff. Data mining Techniques For Marketing, Sales and Customer Support, John Wiley & Sons, Inc. New York, 1997: p.5