How can a C++ header file include implementation?

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.

The true purpose of a header file is to share code amongst multiple source files. It is commonly used to separate declarations from implementations for better code management, but that is not a requirement. It is possible to write code that does not rely on header files, and it is possible to write code that is made up of just header files (the STL and Boost libraries are good examples of that). Remember, when the preprocessor encounters an #include statement, it replaces the statement with the contents of the file being referenced, then the compiler only sees the completed pre-processed code.

So, for example, if you have the following files:

Foo.h:

#ifndef FooH
#define FooH

class Foo
{
public:
    UInt32 GetNumberChannels() const;

private:
    UInt32 _numberChannels;
};

#endif

Foo.cpp:

#include "Foo.h"

UInt32 Foo::GetNumberChannels() const
{
    return _numberChannels;
}

Bar.cpp:

#include "Foo.h"

Foo f;
UInt32 chans = f.GetNumberChannels();

The preprocessor parses Foo.cpp and Bar.cpp separately and produces the following code that the compiler then parses:

Foo.cpp:

class Foo
{
public:
    UInt32 GetNumberChannels() const;

private:
    UInt32 _numberChannels;
};

UInt32 Foo::GetNumberChannels() const
{
    return _numberChannels;
}

Bar.cpp:

class Foo
{
public:
    UInt32 GetNumberChannels() const;

private:
    UInt32 _numberChannels;
};

Foo f;
UInt32 chans = f.GetNumberChannels();

Bar.cpp compiles into Bar.obj and contains a reference to call into Foo::GetNumberChannels(). Foo.cpp compiles into Foo.obj and contains the actual implementation of Foo::GetNumberChannels(). After compiling, the linker then matches up the .obj files and links them together to produce the final executable.

So why is there an implementation in a header?

By including the method implementation inside the method declaration, it is being implicitly declared as inlined (there is an actual inline keyword that can be explicitly used as well). Indicating that the compiler should inline a function is only a hint which does not guarantee that the function will actually get inlined. But if it does, then wherever the inlined function is called from, the contents of the function are copied directly into the call site, instead of generating a CALL statement to jump into the function and jump back to the caller upon exiting. The compiler can then take the surrounding code into account and optimize the copied code further, if possible. 

Does it have to do with the const keyword?

No. The const keyword merely indicates to the compiler that the method will not alter the state of the object it is being called on at runtime.

What exactly is the benefit/point of doing it this way vs. defining the implementation in the CPP file?

When used effectively, it allows the compiler to usually produce faster and better optimized machine code.

It is implicitly declared inline by virtue of being a member function defined within the class declaration. This does not mean the compiler has to inline it, but it means you won't break the one definition rule. It is completely unrelated to const^*. It is also unrelated to the length and complexity of the function.

If it were a non-member function, then you would have to explicitly declare it as inline:

inline void foo() { std::cout << "foo!\n"; }

^* See here for more on const at the end of a member function.

It is perfectly valid to have an implementation of a function in a header file. The only issue with this is breaking the one-definition-rule. That is, if you include the header from multiple other files, you will get a compiler error.

However, there is one exception. If you declare a function to be inline, it is exempt from the one-definition-rule. This is what is happening here, since member functions defined inside a class definition are implicitly inline.

Inline itself is a hint to the compiler that a function may be a good candidate for inlining. That is, expanding any call to it into the definition of the function, rather than a simple function call. This is an optimization which trades the size of the generated file for faster code. In modern compilers, providing this inlining hint for a function is mostly ignored, except for the effects it has on the one-definition-rule. Also, a compiler is always free to inline any function it sees fit, even if it has not been declared inline (explicitly or implicitly).

In your example, the use of const after the argument list signals that the member function does not modify the object on which it is called. In practice, this means that the object pointed to by this, and by extension all class members, will be considered const. That is, trying to modify them will generate a compile-time error.