Normally when using the Text Editor you are in Output View, which provides, with a few exceptions, a view of how the output will appear on the page.
However, as this is the web, the sytsem is maintaining an HTML definition of the text and the formatting. In some circumstances it will be useful to see and work with this directly.
To do so, press the button. You can then work with the HTML.
To return to Output View, press the button again.
Note that you need to be in Output Mode before you can Save changes.