The most common and most likely answer to this crossword clue is the 8 letter word THOUGHTS
I've seen this crossword clue in Independent
T
H
O
U
G
H
T
S
Buddy explains!
The straight part
We know that "some brain activity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case some brain activity = thoughts.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does THOUGHTS mean?
THOUGHTS noun- Form created in the mind, rather than the forms perceived through the five senses; an instance of thinking.
- The operation by which such forms arise or are manipulated; the process of thinking; the agency by which thinking is accomplished.
- A way of thinking (associated with a group, nation or region).