On your Form1 add an event on your button which calls the Form2
private void button1_Click(object sender, EventArgs e)
{
Form2 form2 = new Form2("Hi");
form2.ShowDialog();
}
On your Form2 add a constructor that will accept a string, that will output in your textbox
public Form2(string text)
{
InitializeComponent();
textBox1.Text = text;
}