How does a vector work in C++?

A Vectors in C++ can resize itself when more elements are added. It also allows deletion of elements. 
Below is a very basic idea when array becomes full and user wishes to add an item. 
1) Create a bigger sized memory on heap memory (for example memory of double size). 
2) Copy current memory elements to the new memory. 
3) New item is added now as there is bigger memory available now. 
4) Delete the old memory.
However the actual library implementation may be more complex. If we create a new double sized array whenever current array becomes full (or it is about to become full), and copy current elements to new double sized array, we get amortized time complexity as O(1). So a particular insert operation may be costly, but overall time complexity remains O(1). Please refer Analysis of Algorithm | Set 5 (Amortized Analysis Introduction) for proof. So time complexity of push_back() is O(1).

CPP

// CPP program to illustrate push_back()
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector<int> myvector{ 1, 2, 3, 4, 5 };

    myvector.push_back(6);

    // Vector becomes 1, 2, 3, 4, 5, 6

    for (auto x : myvector)
        cout << x << " ";
}

Output : 

1 2 3 4 5 6 

What is the time complexity of erase() in vector()?
Since erasing an element requires moving other elements (to ensure random access), time complexity of erase is O(n).

CPP

// CPP program to illustrate
// working of erase() function
#include <iostream>
#include <vector>
using namespace std;

int main()
{
    vector<int> myvector{ 1, 2, 3, 4, 5 };

    auto it = myvector.begin();
    myvector.erase(it);

    // Printing the Vector
    for (auto x : myvector)
        cout << x << " ";
    return 0;
}

Output : 

2 3 4 5