In Too Deep - S5-E8
Plot hole: Carter is apparently just learning about Feynman's Day, which Allison explains as "Eureka's version of April Fool's Day." It's highly improbable that Carter could have lived in Eureka for five years and still be oblivious of this, especially given all of the hijinks that happen.
Chosen answer: It's basically just a type of suit that's made for whatever special project they're working on. No different than a lab coat, hazmat suit, fire coat, etc.