Extelligence is a concept
that helps to explain the development
of a mind
Essentially, the theory of extelligence is that a mind requires intelligence to develop (you must draw the difference between brain and mind here), but it also requires interaction with other intelligence. This external intelligence that it interacts with is called extelligence.
Compare humans and dolphins. Dolphins show definate signs of intelligence, as do humans (or most of us anyway), however we are developing ideas and inventing things while all they are doing is playing around in the water.
One possible explanation for this is that dolphins have a larger environment but smaller numbers, so there is less interaction.
Extelligence is a complex theory, but I hope this brief description is of some help.