What does it mean to be "sh compatible"?

I've seen the phrase "sh compatible" used usually in reference to shells. I'm not sure if it also applies to the programs that might be run from within shells. What does it mean for a shell or other program to be "sh compatible"? What would it mean to be "sh incompatible"? Edit: This question asking the difference between bash and sh is very relevant: Difference between sh and bash I'd still like a direct answer to what it means to be "sh compatible". A reasonable expectation might be that "sh compatible" means "implements the Shell Command Language" but then why are there so many "sh compatible" shells and why are they different?