What is the id( ) function used for?

Your post asks several questions:

What is the number returned from the function?

It is "an integer (or long integer) which is guaranteed to be unique and constant for this object during its lifetime." (Python Standard Library - Built-in Functions) A unique number. Nothing more, and nothing less. Think of it as a social-security number or employee id number for Python objects.

Is it the same with memory addresses in C?

Conceptually, yes, in that they are both guaranteed to be unique in their universe during their lifetime. And in one particular implementation of Python, it actually is the memory address of the corresponding C object.

If yes, why doesn't the number increase instantly by the size of the data type (I assume that it would be int)?

Because a list is not an array, and a list element is a reference, not an object.

When do we really use id( ) function?

Hardly ever. You can test if two references are the same by comparing their ids, but the is operator has always been the recommended way of doing that. id( ) is only really useful in debugging situations.

That's the identity of the location of the object in memory...

This example might help you understand the concept a little more.

foo = 1
bar = foo
baz = bar
fii = 1

print id(foo)
print id(bar)
print id(baz)
print id(fii)

> 1532352
> 1532352
> 1532352
> 1532352

These all point to the same location in memory, which is why their values are the same. In the example, 1 is only stored once, and anything else pointing to 1 will reference that memory location.

id() does return the address of the object being referenced (in CPython), but your confusion comes from the fact that python lists are very different from C arrays. In a python list, every element is a reference. So what you are doing is much more similar to this C code:

int *arr[3];
arr[0] = malloc(sizeof(int));
*arr[0] = 1;
arr[1] = malloc(sizeof(int));
*arr[1] = 2;
arr[2] = malloc(sizeof(int));
*arr[2] = 3;
printf("%p %p %p", arr[0], arr[1], arr[2]);

In other words, you are printing the address from the reference and not an address relative to where your list is stored.

In my case, I have found the id() function handy for creating opaque handles to return to C code when calling python from C. Doing that, you can easily use a dictionary to look up the object from its handle and it's guaranteed to be unique.

Rob's answer (most voted above) is correct. I would like to add that in some situations using IDs is useful as it allows for comparison of objects and finding which objects refer to your objects.

The later usually helps you for example to debug strange bugs where mutable objects are passed as parameter to say classes and are assigned to local vars in a class. Mutating those objects will mutate vars in a class. This manifests itself in strange behavior where multiple things change at the same time.

Recently I had this problem with a Python/Tkinter app where editing text in one text entry field changed the text in another as I typed :)

Here is an example on how you might use function id() to trace where those references are. By all means this is not a solution covering all possible cases, but you get the idea. Again IDs are used in the background and user does not see them:

class democlass:
    classvar = 24

    def __init__(self, var):
        self.instancevar1 = var
        self.instancevar2 = 42

    def whoreferencesmylocalvars(self, fromwhere):
        return {__l__: {__g__
                    for __g__ in fromwhere
                        if not callable(__g__) and id(eval(__g__)) == id(getattr(self,__l__))
                    }
                for __l__ in dir(self)
                    if not callable(getattr(self, __l__)) and __l__[-1] != '_'
                }

    def whoreferencesthisclassinstance(self, fromwhere):
        return {__g__
                    for __g__ in fromwhere
                        if not callable(__g__) and id(eval(__g__)) == id(self)
                }

a = [1,2,3,4]
b = a
c = b
democlassinstance = democlass(a)
d = democlassinstance
e = d
f = democlassinstance.classvar
g = democlassinstance.instancevar2

print( 'My class instance is of', type(democlassinstance), 'type.')
print( 'My instance vars are referenced by:', democlassinstance.whoreferencesmylocalvars(globals()) )
print( 'My class instance is referenced by:', democlassinstance.whoreferencesthisclassinstance(globals()) )

OUTPUT:

My class instance is of <class '__main__.democlass'> type.
My instance vars are referenced by: {'instancevar2': {'g'}, 'classvar': {'f'}, 'instancevar1': {'a', 'c', 'b'}}
My class instance is referenced by: {'e', 'd', 'democlassinstance'}

Underscores in variable names are used to prevent name colisions. Functions use "fromwhere" argument so that you can let them know where to start searching for references. This argument is filled by a function that lists all names in a given namespace. Globals() is one such function.

I am starting out with python and I use id when I use the interactive shell to see whether my variables are assigned to the same thing or if they just look the same.

Every value is an id, which is a unique number related to where it is stored in the memory of the computer.