Winforms binding question

I am relatively new to binding in win forms. In order to learn the subject I setup the following test application. A basic winform with a ListBox and a Button.

public partial class Form1 : Form
{
    public List<String> stringList = new List<String>();

    public Form1()
    {
        InitializeComponent();
        stringList.Add("First");
        listBox1.DataSource = stringList;
    }

    private void button1_Click(object sender, EventArgs e)
    {
        stringList.Add("Second");
    }
}

The string "First" shows in listBox1 on application launch. However, when I push the button which adds a new string to the stringList the new item is not shown in listBox1. Could anyone help me understand the basics of collection data binding?