What does the EEG measure?

Brain activity. Eeg is a test of physiological function, and records brain electical activity (like electrocardiogram for heart). It is used to check for seizure activity, to evaluate various headache issues, to check patients with memory loss, evaluated folks with brain infections, and also confirm brain death.
Electrical activity. Eeg measures the electrical activity of nerves in the brain, most prominently the postsynaptic potentials generated by neurons at the top of the gyri (the "folds" of tissue on the brain surface).