A pointer is a variable that contains the address of another variable. This allows you to reference another variable indirectly. For example, in C:

// x is an integer variable
int x = 5;
// xpointer is a variable that references (points to) integer variables
int *xpointer;
// We store the address (& operator) of x into xpointer.
xpointer = &x;
// We use the dereferencing operator (*) to say that we want to work with
// the variable that xpointer references
*xpointer = 7;
if (5 == x) {
    // Not true
} else if (7 == x) {
    // True since we used xpointer to modify x
}

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...

A variable itself is a pointer to data

No, it is not. A variable represents an object, an lvalue. The concept of lvalue is fundamentally different from the concept of a pointer. You seem to be mixing the two.

In C it is not possible to "rebind" an lvalue to make it "point" to a different location in memory. The binding between lvalues and their memory locations is determined and fixed at compile time. It is not always 100% specific (e.g. absolute location of a local variable is not known at compile time), but it is sufficiently specific to make it non-user-adjustable at run time.

The whole idea of a pointer is that its value is generally determined at run time and can be made to point to different memory locations at run time.

How do pointers to pointers work in C?

First a pointer is a variable, like any other variable, but that holds the address of a variable.

A pointer to a pointer is a variable, like any other variable, but that holds the address of a variable. That variable just happens to be a pointer.

When would you use them?

You can use them when you need to return a pointer to some memory on the heap, but not using the return value.

Example:

int getValueOf5(int *p)
{
  *p = 5;
  return 1;//success
}

int get1024HeapMemory(int **p)
{
  *p = malloc(1024);
  if(*p == 0)
    return -1;//error
  else 
    return 0;//success
}

And you call it like this:

int x;
getValueOf5(&x);//I want to fill the int varaible, so I pass it's address in
//At this point x holds 5

int *p;    
get1024HeapMemory(&p);//I want to fill the int* variable, so I pass it's address in
//At this point p holds a memory address where 1024 bytes of memory is allocated on the heap

There are other uses too, like the main() argument of every C program has a pointer to a pointer for argv, where each element holds an array of chars that are the command line options. You must be careful though when you use pointers of pointers to point to 2 dimensional arrays, it's better to use a pointer to a 2 dimensional array instead.

Why it's dangerous?

void test()
{
  double **a;
  int i1 = sizeof(a[0]);//i1 == 4 == sizeof(double*)

  double matrix[ROWS][COLUMNS];
  int i2 = sizeof(matrix[0]);//i2 == 240 == COLUMNS * sizeof(double)
}

Here is an example of a pointer to a 2 dimensional array done properly:

int (*myPointerTo2DimArray)[ROWS][COLUMNS]

You can't use a pointer to a 2 dimensional array though if you want to support a variable number of elements for the ROWS and COLUMNS. But when you know before hand you would use a 2 dimensional array.