In plain and simple terms, what is the POSIX standard and why does it matter?
Also if I have two systems that are 100% POSIX compatible, would code compiled for one work on the other without a problem?
It defines an interface (POS I X) to a computing environment (POSI X) that is meant to be portable (P OSIX) across operating systems (P OS IX). This interface extends across both user (commands) and program (libraries) space, and allows both source code as well as shell scripts to work in any given environment.
If the program only uses POSIX capabilities then it should work on any POSIX-compliant OS.