EEG or trace of the brain is used to pick up electrical brain activity in the brain by placing leads on the head. It is very similar principal to ECG (Electrocardiogram), which picks up electrical activity of the heart.
Epilepsy, though is primarily a clinical diagnosis as EEG can be normal in children with Epilpepsy and many normal people (upto 5%) can have abnormal EEG. It is helpful though to know the type of seizures, their origin etc.
Various types of EEG are described in this section in the excellent Epilepsy Society website https://www.epilepsysociety.org.uk/eeg-electroencephalogram#.XD-4qc_7St8