An epileptic seizure is a sudden, involuntary, and usually short change in behavior, movement, sensation, and/or consciousness (alertness) associated to an abnormal electrical pattern (like an electrical "storm") in the brain. The abnormal electrical pattern can usually be seen at the time of the seizure in an EEG (electro-encephalogram).
A nonepileptic seizure is an episode or event that may look and feel similar to what is described above (epileptic seizures), but it happens without the abnormal electrical changes that happen during epileptic seizures.
This means that to an observer, a nonepileptic seizure might look very similar to an epileptic seizure, but if you were to connect an EEG to record electrical activity in the brain during the nonepileptic seizure, you would not see the type of abnormal electrical activity seen in epilepsy with a nonepileptic seizure.