A Brain Dump is, literally getting all the stuff that's buzzing around in your head onto paper or into a document.
It doesn't need to be well-ordered, but may well be the start of an organizing process.
One popular approach to taking the PMP exam, before 2021 was to start with a Brain Dump of all the hard-to-recall things like formulas.
PMI centers would provide pen and paper and, at the start of the exam, candidates could quickly write down everything they had stuffed into their brains just before the exam, so that the information was there when they needed it, in the exam.
The idea behind it has some validity:
Under the stress of answering a question, recall of something like formula can be hard. And, if there are two similar questions, it could be easy for some candidates to mix up formulas or processes, or recall them incorrectly.
The brain dump at the start has none of the triggers - so you can get the information on a piece of paper correctly - then read off it when you need the information in the exam. Plus, maybe if you do have a mental block over one formula, say, you can shove it into your short-term memory the last thing before going into the exam... and then empty it back out as soon as the exam starts.
The Problem with the Brain Dump Method
It works for some people... but not for others. For them, it's just a (literal) waste of their precious exam time.
Yet too many 'PMP advice sites' advocated the Brain Dump technique unequivocally. They offered no practical advice and possibly had not thought out the pros and cons. They simply parrotted advice from other sources, uncritically.
Brain Dump in the Current exam
There is no pen and paper in the current exam. There is just an online whiteboard that you can use as a scratchpad. This is slower to use and less efficient. It diminishes the argument for the Brain Dump method and makes it suitable for fewer people.
Our Advice
I hope you plan to do some practice exams. Try out the Brain Dump approach. Only one person can determine whether it will help you in the exam, or just waste some of your time... No, not me. YOU!
Brain Dump as Learning Technique
Whether you choose to use the Brain Dump method to help you in your exam or not, there is a very real use for it in your preparation.
At the start of a Learning Session
At the start of a learning session (whether at the beginning of your campaign, or a the end) do a brain dump of everything you know about the topic you are going to study in the session. Paper and pen or software app - whichever you prefer. If in doubt: go with pen and paper.
Next, organize it. I recommend a mind map.
Then compare it to the ECO and the content of your primary reference materials (PMBOK Guide, Agile Practice Guide, Scrum Guide, ATP course notes, Prep Book). Where are the gaps, and what areas do you still not understand fully?
Use this to guide your study priorities.
At the End of a Learning Session
Repeat your brain dump and organizing process for this topic. This will reinforce what you have learned.