It means to have a fit, whether it be epileptic or emotional. To forego rationality and opt for spasmodic movements, arms flailing, and utterances of an incoherent nature. Likewise, it is the behavior of people who get upset when they don't understand something.
Ignorant people will chuck a spaz when you pitch your latest theory on anti-matter and the black hold vortices. OR
I need some heroin now and if you don't give it to me I'll chuck a spaz.