Tony Buzan brought mind mapping to public attention
Mind Mapping is one of the best tools for brainstorming
Here is Tony Buzan himself speaking to you about the importance of learning how to use mind maps.
The great thing about using a mind map for brainstorming is that you are diagramming your ideas the same way the brain makes associations. Those associations are how a brain thinks and remembers. The drawing of the mind map draws out ideas from everyone participating because the process fits so naturally with how we think. Then it helps further with building more associations and memory.
The title's of Buzan's books give you a good idea how completely he believes in the connection between the brain and mind mapping: The Mind Map Book (which I recommend as a first book to read on the subject)