Ok, not a C/C++ expert by any means, but I thought the point of a header file was to declare the functions, then the C/CPP file was to define the implementation.
How
Even in plain C, it is possible to put code in a header file. If you do it, you usually need to declare it static or else multiple .c files including the same header will cause a "multiply defined function" error.
The preprocessor textually includes an include file, so the code in an include file becomes part of the source file (at least from the compiler's point of view).
The designers of C++ wanted to enable object-oriented programming with good data hiding, so they expected to see lots of getter and setter functions. They didn't want an unreasonable performance penalty. So, they designed C++ so that the getters and setters could not only be declared in the header but actually implemented, so they would inline. That function you showed is a getter, and when that C++ code is compiled, there won't be any function call; code to fetch out that value will just be compiled in place.
It is possible to make a computer language that doesn't have the header file/source file distinction, but just has actual "modules" that the compiler understands. (C++ didn't do that; they just built on top of the successful C model of source files and textually included header files.) If source files are modules, it would be possible for a compiler to pull code out of the module and then inline that code. But the way C++ did it is simpler to implement.