What is the "Illegal Instruction: 4" error and why does "-mmacosx-version-min=10.x" fix it?

From the Apple Developer Forum (account required):

"The compiler and linker are capable of using features and performing optimizations that do not work on older OS versions. -mmacosx-version-min tells the tools what OS versions you need to work with, so the tools can disable optimizations that won't run on those OS versions. If you need to run on older OS versions then you must use this flag.

"The downside to -mmacosx-version-min is that the app's performance may be worse on newer OS versions then it could have been if it did not need to be backwards-compatible. In most cases the differences are small."

The "illegal instruction" message is simply telling you that your binaries contain instructions the version of the OS that you are attempting to run them under does not understand. I can't give you the precise meaning of 4 but I expect that is internal to Apple.

Otherwise take a look at these... they are a little old, but probably tell you what you need to know

How does 64 bit code work on OS-X 10.5?
what does macosx-version-min imply?

I'm consciously writing this answer to an old question with this in mind, because the other answers didn't help me.

I got the Illegal Instruction: 4 while running the binary on the same system I had compiled it on, so -mmacosx-version-min didn't help.

I was using gcc in Code Blocks 16 on Mac OS X 10.11.

However, turning off all of Code Blocks' compiler flags for optimization worked. So look at all the flags Code Blocks set (right-click on the Project -> "Build Properties") and turn off all the flags you are sure you don't need, especially -s and the -Oflags for optimization. That did it for me.

I found my issue was an improper
if (leaf = NULL) {...}
where it should have been
if (leaf == NULL){...}

Check those compiler warnings!