What's the difference between a const member function and a non-const member function?

I am very confused about the const version and non-const version member function like below:

value_type& top() { return this.item }
const value_type& top() const { return this.item }

What is the difference between these two functions? In what situation would they be used?

In short, they're used to add 'const correctness' to your program.

value_type& top() { return this.item }

This is used to provide mutable access to item. It is used so you can modify the element in the container.

For example:

c.top().set_property(5);  // OK - sets a property of 'item'
cout << c.top().get_property();  // OK - gets a property of 'item'

One common example for this pattern is returning mutable access to an element with vector::operator[int index].

std::vector<int> v(5);
v[0] = 1;  // Returns operator[] returns int&.

On the other hand:

const value_type& top() const { return this.item }

This is used to provide const access to item. It's more restrictive than the previous version - but it has one advantage - you can call it on a const object.

void Foo(const Container &c) {
   c.top();  // Since 'c' is const, you cannot modify it... so the const top is called.
   c.top().set_property(5);  // compile error can't modify const 'item'.
   c.top().get_property();   // OK, const access on 'item'. 
}

To follow the vector example:

const std::vector<int> v(5, 2);
v[0] = 5;  // compile error, can't mutate a const vector.
std::cout << v[1];  // OK, const access to the vector.

The const-qualified member function will be called if the member function is called on an object that is const-qualified.

The non-const-qualified member function will be called if the member function is called on an object that is not const-qualified.

For example:

MyStack s;
s.top(); // calls non-const member function

const MyStack t;
t.top(); // calls const member function

Note that the same rules apply when calling a member function on a reference to an object or through a pointer to an object: if the pointer or reference is to a const object, the const member function will be called; otherwise the non-const member function will be called.