Central nervous system (CNS) fatigue happens during all muscular contractions (in some more than others) and takes a varied length of time to recover (depending on the workout). Therefore, performing another set too soon after the previous one leads to reduced levels of motor unit recruitment, which stops all of the muscle fibers of the muscle from being activated and therefore trained.

https://medium.com/@SandCResearch/do-short-rest-periods-help-or-hinder-muscle-growth-7859e0c4adfd