This phrase is seriously abused and it needs to stop because our field has anything but standardized and well-known competencies that we expect people to know before they commit anything.
Compiling main() with an assignment and a print is technically programming, but has extremely little to do with what is actually being developed in real products. You aren't going to give anyone a job if this is all they can do. As soon as you get out of the absolute basics (IMO, if/for/assignment/operators), your demands are simply arbitrary with what you think will indicate that someone can do the job.
You might only consider someone who can pass FizzBuzz as a 'real programmer'. Someone else might only consider someone who knows and can implement advanced patterns and quickly absorb an unfamiliar API as a 'real programmer'. Programming-Genius-32 might only think someone's a 'real programmer' when he can implement every algorithm from MIT's curriculum from scratch.
And if I had to make a wild guess, I would guess that people create their own standards of what a 'real programmer' is based on things they have already solved or things they read from someone else. Then they go make hiring decisions based on this standard. It is very likely that someone can look down on many of us and call us fake programmers because they're just so much further ahead.
Convincing someone that you are a real programmer of a certain skill level is a social exercise, not a technical one.