textbox append data

You want that your UI get updated one by one.Why are you not doing with javascript using settimeout.
Although, you can also invoke ajax call to get the data from server, using settimeout and update the UI one by one.

[Added]

Its better, if you do this at client side. But for server side also
you need to use setTimeout( initiateAjax(), timeout ) which
is a javascript method. initiateAjax() will initiate ajax call and get the data from server and update the UI, timeout is in miliseconds. Means initiateAjax() will be called after timeout miliseconds. So you need to do looping over it.
And about ajax call, you can use jQuery call, as I have used in my below article.
Client Templating with jQuery


For details about setTimeout, have a look
Click here[^]

[/Added]

Instead of having the entire for loop in your button click event, I think you want the following...

This logic will help you display which iteration you are currently in. It will increment the value of "i"(_currentIValue) each time you press the button and the value in the textbox will reflect the current state of "i"(_currentIValue) at the end of each execution of this method.

private int _currentIValue = 0;

protected void buttonClickHandler(object sender, EventArgs e)
{
    // Do your processing here...
    // Since you have your loop 0 to 100 in your example
    if( _currentIValue < 100 )
    {
        //TextBox1.Text = _currentIValue.ToString(); // This line will replace the text
        TextBox1.Text = TextBox1.Text + Environment.NewLine + _currentIValue.ToString();
        _currentIValue ++;
        // Can also be written in one line
        // TextBox1.Text = _currentIValue++;
    }
}