First you need to decide on what event will it be saved. Either when check changed or button was clicked. Then where/how you want to save it- to a file, database or other.
assume it is a button click event and saved to a file and method called is SaveText():
you only need to test for when checkbox.Checked is true
void SaveText()
{
string txt = textbox.Text;
if(checkbox.Checked){
}
}