Understanding the C++ Templates

#include <iostream>
#include <string>
#include <vector>
#include <stdexcept>
using namespace std;
//We will define the Stack<> class and implement generic methods
//to push and pop the elements from the stack
template <class T>
    class Stack {
    private:
        vector<T> elementsToPushAndPop;
    public:
        void push(T const&);
        void pop();
        T top() const;
        bool empty() const {
            return elementsToPushAndPop.empty();
        }
};
template <class T>
void Stack<T>::push (T const& elem) {
    // we can append the copy of the element that we passed
    elementsToPushAndPop.push_back(elem);
}
template <class T>
void Stack<T>::pop () {
    // if the stack is empty, we can throw an exception
    if (elementsToPushAndPop.empty()) {
        throw out_of_range("Stack<>::pop(): empty stack");
    }
    // then we can remove the last element
    elementsToPushAndPop.pop_back();
}
template <class T>
T Stack<T>::top () const {
    // if the stack is empty, we can throw an exception
    if (elementsToPushAndPop.empty()) {
        throw out_of_range("Stack<>::top(): empty stack");
    }
    // then we can return a copy of the last element
    return elementsToPushAndPop.back();
}
int main(){
    // Let's create a stack of integer elements
    Stack<int> stackIntegers;
    // now we can keep adding to the stack
    stackIntegers.push(500);
    stackIntegers.push(501);
    cout << stackIntegers.top() << endl;
    if(stackIntegers.empty()){
        cout << "The stack is empty." << endl;
    } else {
        cout << "The stack is not empty." << endl;
    }
    // Let's remove one element from our stack
    stackIntegers.pop();
    // and see the output
    cout << stackIntegers.top() << endl;
    // after that we can check whether the stack is empty
    if(stackIntegers.empty()){
        cout << "The stack is empty." << endl;
    } else {
        cout << "The stack is not empty." << endl;
    }
    // and see the output
    cout << stackIntegers.top() << endl;
    // Let's keep removing the stack elements
    try {
        // this removes 500
        stackIntegers.pop();
        // if we try to remove the element again, it will throw an exception
        // that we can now catch
        stackIntegers.pop();
    } catch (exception const& excep) {
        cerr << "Exception: " << excep.what() << endl;
        return -1;
    }
    
    return 0;
}