A PoC or a proof of concept is a simple implementation which demonstrates an idea, but omits nonessential functionality to focus on solving just the important problem.
A PoC or a proof of concept is a simple program which demonstrates an idea, enough to decide whether it makes sense to explore it further to develop a complete product or service, or to demonstrate a bug in an isolated context. Security researchers also use this term for programs which demonstrate the existence of an exploit, but which typically then only use it to do something benign, like run the calculator app or show that they can make the vulnerable system print "hello world", for example.