When you search the web (I like the Google define: option) the definitions that stand out to me are:
Business intelligence (BI) is a broad category of application programs and technologies for gathering, storing, analyzing, and providing access to data to help enterprise users make better business decisions. BI applications include the activities of decision support, query and reporting, online analytical processing (OLAP), statistical analysis, forecasting, and data mining.
Business intelligence (BI) is the process of gathering information in the field of business. It can be described as the process of enhancing data into information and then into knowledge.Business intelligence is carried out to gain sustainable competitive advantage, and is a valuable core competence in some instances.
Wikipedia provides the definition or analogy that I like and have used before when explaining the concept, that BI can be likened to an evolution of data to knowledge. "Decision Support" is also a good simple explanation.
The first definition although accurate, does seem to open up a can of worms as it defines BI in other obscure and perhaps ambiguous terms, for example what is "Data Mining"? (this returns 23 separate entries!).
A very good introductory book I have read also defines BI in terms of data to knowledge evolution. The book "Business Intelligence The Savvy Manager's Guide" It goes on to mention that BI is more than just a toolset, but requires the correct processes and people. The more most important statement however is that "the value of BI is realised in the context of profitable business action". This is crucial and the book goes on to labour this point, that if you cant use the information/knowledge that a BI system provides it is worthless.
This is the primary facet that should be held when producing a BI System and really forms the basis of the mission statement for any BI solution.