What exactly is a C pointer if not a memory address?

The C standard does not define what a pointer is internally and how it works internally. This is intentional so as not to limit the number of platforms, where C can be implemented as a compiled or interpreted language.

A pointer value can be some kind of ID or handle or a combination of several IDs (say hello to x86 segments and offsets) and not necessarily a real memory address. This ID could be anything, even a fixed-size text string. Non-address representations may be especially useful for a C interpreter.

I'm not sure about your source, but the type of language you're describing comes from the C standard:

6.5.3.2 Address and indirection operators
[...]
3. The unary & operator yields the address of its operand. [...]

So... yeah, pointers point to memory addresses. At least that's how the C standard suggests it to mean.

To say it a bit more clearly, a pointer is a variable holding the value of some address. The address of an object (which may be stored in a pointer) is returned with the unary & operator.

I can store the address "42 Wallaby Way, Sydney" in a variable (and that variable would be a "pointer" of sorts, but since that's not a memory address it's not something we'd properly call a "pointer"). Your computer has addresses for its buckets of memory. Pointers store the value of an address (i.e. a pointer stores the value "42 Wallaby Way, Sydney", which is an address).

Edit: I want to expand on Alexey Frunze's comment.

What exactly is a pointer? Let's look at the C standard:

6.2.5 Types
[...]
20. [...]
A pointer type may be derived from a function type or an object type, called the referenced type. A pointer type describes an object whose value provides a reference to an entity of the referenced type. A pointer type derived from the referenced type T is sometimes called ‘‘pointer to T’’. The construction of a pointer type from a referenced type is called ‘‘pointer type derivation’’. A pointer type is a complete object type.

Essentially, pointers store a value that provides a reference to some object or function. Kind of. Pointers are intended to store a value that provides a reference to some object or function, but that's not always the case:

6.3.2.3 Pointers
[...]
5. An integer may be converted to any pointer type. Except as previously specified, the result is implementation-defined, might not be correctly aligned, might not point to an entity of the referenced type, and might be a trap representation.

The above quote says that we can turn an integer into a pointer. If we do that (that is, if we stuff an integer value into a pointer instead of a specific reference to an object or function), then the pointer "might not point to an entity of reference type" (i.e. it may not provide a reference to an object or function). It might provide us with something else. And this is one place where you might stick some kind of handle or ID in a pointer (i.e. the pointer isn't pointing to an object; it's storing a value that represents something, but that value may not be an address).

So yes, as Alexey Frunze says, it's possible a pointer isn't storing an address to an object or function. It's possible a pointer is instead storing some kind of "handle" or ID, and you can do this by assigning some arbitrary integer value to a pointer. What this handle or ID represents depends on the system/environment/context. So long as your system/implementation can make sense of the value, you're in good shape (but that depends on the specific value and the specific system/implemenation).

Normally, a pointer stores an address to an object or function. If it isn't storing an actual address (to an object or function), the result is implementation defined (meaning that exactly what happens and what the pointer now represents depends on your system and implementation, so it might be a handle or ID on a particular system, but using the same code/value on another system might crash your program).

That ended up being longer than I thought it would be...

In this picture,

pointer_p is a pointer which is located at 0x12345, and is pointing to a variable variable_v at 0x34567.