A squeezure is the literal combination of a squee and a seizure. It usually happens when a fangirl witnesses something that she really, really likes, and consists of uncontrollable shaking, squeeing, and perhaps drooling. If you witness a fangirl displaying these behaviors, do not panic, she is just happy.
*Dramatic scene in anime plays*
Fangirl: *falls down, squeeing, shaking, and drooling uncontrollably*
Boy: Oh my god, Is that girl okay?
Other fangirl: Yes, she's just having a squeezure.