In the prefaces of many Bible translations, there are notes that describe the origin of these headers:
As an aid to the reader, sectional headings have been inserted. They are not to be regarded as part of the biblical text and are not intended for oral reading. It is the committee’s hope that these headings may prove more helpful to the reader than the traditional chapter divisions, which were introduced long after the Bible was written. (NIV 2011 preface, emphasis added)
These section headings are added by the translation committees (or, on occasion, the publishers) to break up the text and help readers find what they are looking for. It becomes clear that these aren't "part of the text" when we realize just how much they vary. Here's a quick sampling for Romans 1:16:
- ESV: "The Righteous Shall Live by Faith"
- KJV: None
- NASB: None
- NIV: None
- NLT: None
- RSV: "The Power of the Gospel"
But it's not just the section headings that aren't part of the original text. As the NIV preface indicates, even the chapter divisions (and verse divisions) are relatively recent innovations – the chapters we use today are based on a system developed by Stephen Langton in the 13th century. And even these divisions are not fully standardized – see Are chapter and verse divisions international? for some exceptions.
So consider section headings as simply aids to the reader, not as components of the original text. They should also be regarded as separate from the chapter and verse divisions.
N. B.: There are some "headings" in the Bible that are commonly considered "part of the text" – the titles of Psalms, such as in Psalm 14, "To the choirmaster. Of David" (ESV). These are usually considered "canonical" but not necessarily original – some of them may have been added by editors in the centuries leading up to the apostolic era. For more on this, see Mark David Futato, Interpreting the Psalms, pages 119–122.