The Text Options button can be found next to the Bible drop-down selector on the passage results page (for example, see the passage results page for John 3:16). It allows you to adjust the way that the Bible passage is displayed in your web browser by toggling on/off page elements like headings, verse numbers, and footnotes.
Clicking or tapping the Text Options button (which looks like a gear) lists several different text annotations that can be toggled on or off:
Clicking the settings icon next to the Study This button causes those elements (if they are present in the Bible passage you're looking at) to be displayed. Unchecking them removes those elements from the passage.
Checking Footnotes, Cross References, Verse Numbers, or Headings adds or removes those elements from the passage you're viewing. The Red Letter option causes words spoken by Jesus to be displayed in red, as long as you are using a Bible that supports this feature.