Your normal mode of thinking involves quickly dismissing many ideas, thoughts, hypothesis, etc., which is necessary to actually get stuff done. Brainstorming isn't a good idea when you're trying to think of a way to cross a road quickly.
Brainstorming let's you freely associate by postponing your own judgement. It gets you into corners of your mind you wouldn't visit if you were actively trying to solve the problem. Of course that is also a way of 'thinking': the point is that you get into a different mindset and think in different ways.
As far as I know that is common, but I would also still describe it as a group activity, even though the initial idea generation is done solo. The process could for instance be:
* Do a short exercise to prime everyone to 'let go of their default mindset' (you can leave this out if everyone is experienced in doing this, although it should usually be fun)
* Have everyone put their own ideas to paper, within a reasonable amount of time, while together in the same room, but without communicating about them
* Together, group the results: determine overlaps and outliers.
* Then discuss the results together
In the last phase, the first exercise and the resulting mindset still has some effect: people will be less protective of their specific ideas, because of the mindset that generated them, which can easily be blamed for 'silly' ideas. Some outliers can therefore be dismissed easily. On the other hand, people will more seriously consider ideas they might otherwise have dismissed as 'silly' right after they were uttered. Some outliers may prove to be very valuable and a group brainstorm wouldn't have resulted in them.
Brainstorming, as I understand the term, is used to describe this entire process of idea generation and evaluation. Not just the phase/mindset when generating ideas and not just when that happens in a group together. Perhaps this school of thought is more regionally limited than I know and this is indeed not generally known as 'brainstorming'.
Brainstorming let's you freely associate by postponing your own judgement. It gets you into corners of your mind you wouldn't visit if you were actively trying to solve the problem. Of course that is also a way of 'thinking': the point is that you get into a different mindset and think in different ways.