Question

as we use pointers in the argument list of functions like

void f(int *); 

this means that this function will receive a pointer to an integer
but what does this means

void f(int ***); 

and

void f(int **=0)

Answer 1

void f(int ***); 

means that the function receives a pointer to a pointer to a pointer to an int. This would work with it:

int x=42;
int *px=&x;
int **ppx=&px;
int ***pppx=&ppx;
f(pppx);

Now about the 2nd one, its a function that receives a pointer to a pointer to an int, and if you give it nothing, it defaults to 0.

int x=42;
int *px=&x;
int **ppx=&px;
f(ppx);  // pt to pt to x
f();     // same as f(0)

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UPDATE:

A practical application of this kind of double pointers is a memory allocation routine like:

bool alloc(T **mem, int count);

This function returns true/false depending on whether or not it worked and would update the pointer you pass in with the real memory address, like this:

T *mem;
verify(alloc(&mem, 100));

You pass in an uninitialized pointer and the function can overwrite it with a real value because you passed a pointer to the actual pointer. At the end, mem contains a pointer to valid memory.

Another application, more common but a lot less enlightening, is an array of arrays (so-called jagged arrays).