The Quick Tag Editor starts in Insert HTML mode when you open it without anything selected. It opens showing a pair of angle brackets with the insertion point between them. You can enter arbitrary HTML strings in the editor in this mode, including multiple tags and text or other content between tags. When you close the editor, the HTML you've entered is inserted at the insertion point; if you leave tags unclosed, the corresponding closing tags are added automatically.
To switch from Insert HTML mode to Edit Tag mode, use the Control+T (Windows) or Command+T (Macintosh) keyboard shortcut again. See About Edit Tag mode. To switch to Wrap Tag mode from Insert HTML mode, use the keyboard shortcut twice. See About Wrap Tag mode.