Intelligence is defined as the ability of a mind to think, reason, acquire, and apply knowledge.
It is also used to describe incorporeal minds, especially in the Intelligent Design debate, which postulates that an Intelligence must have created to universe. Therefore it can mean God, Allah, Saint Peter, Vishnu, or the Flying Spaghetti Monster, depending upon which religion you prescribe yourself to.
Intelligence as part of a brain
Biologically speaking, intelligence is that property that results when neurons get together to form a complex brain. The neurons act together to form patterns that represent information. Other parts of the brain can recall and change that information, or put it to use.
The intelligent brain is also good at reasoning. In other words, it can detect patterns between seemingly unconnected peices of information, form links, and theorise about them.
The extremely intelligent brain also exibits consciousness. Consiousness can be loosely defined as knowledge of one's self, and the desire to ask the question "Who am I?". So far as science can tell, Homo Sapiens is the only creature that asks this question, and then seeks to answer it for himself. Some find religion, some use science, some use philosophy, to answer this question.