Brain cells, also known as neurons, communicate via electrical impulses. This communication never ceases as long as a human is clinically considered to be alive. In fact, EEG is conventially used to confirm brain death in a persistent coma, where electrical activity is consistently at a bare minimum.
Figure A on the left shows an EEG recording of a healthy awake person in eyes open condition. The electric activity shows up as wavy lines on the EEG recording.
Figure B shows the EEG of a person during a phase of deep sleep. Extended deep sleep phases are extremely important for maintaining overall brain health as the brain switches into "repair mode" during those phases with a significantly increased immune response.
Both recordings show distinct characteristics linked to the current cognitive state. These characteristics generalize over different individuals and populations, often even to brains of other mammals.