This is the 13248th most frequent Russian word.
мозговая
"Мозговая" translates to "brain" or "cerebral" in English, depending on context.
Here 'мозговая' is used as an adjective to describe 'active' which refers to activity pertaining to the brain.
Мозговая активность усиливается при решении сложных задач.
Brain activity increases when solving complex problems.
In this sentence, 'мозговая' (brain-related) describes 'surgery' (хирургия), indicating its specialization.
Он занимается мозговой хирургией уже десять лет.
He has been practicing brain surgery for ten years.
The term 'мозговой' (brain-related) in 'brainstorm' conveys the idea of intellectual effort or mental activity.