The typical EEG-waves originate in the cortex of the brain. Neurologists interpret them as synchronous electrical potentials produced by groups of cells rather than individuals. The waves reflect potentials from nerve cell regions called dendrites directly behind the synapses (more). Electrical activity from deeper regions of the brain does not reach the surface and can thus not be distinguished in the EEG. The electrical activity measured by the EEG lies in regions between 1 and 100 mikroV. This means that the whole thing is quite sensitive towards disturbances and needs some care when used.
What a doctor normally sees with an awake adult are alpha-waves (frequency 8-13Hz). Beta-waves (13-30Hz) occur infrequently in all subjects. Sleeping adults and young children between 18 months and 5 years of age tend to produce theta-waves (4-7Hz). Newborns and adults in deep sleep can show delta-waves (below 4Hz). Older children and awake adults with delta-waves usually have a severe neurological problem (more).

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Some background science here: Learn about eeg in medicine and why it can de used for BCI-control.