In Biblical and classical scholarship this sort of thing is often called a capitulum, which confusingly is also a term for an entire chapter. However, I think it would be a bit affected to use that word in the context of modern literature, and something like "chapter title" or "chapter summary" would be more natural. Or, given that capitulum literally means a little head, a "heading".
According to The Latin New Testament by H. A. G. Houghton (OUP, 2016) at chapter 8,
In manuscripts, they are introduced by a variety of terms including breues, breuiarium, tituli, elenchus, breues causae, capitulatio, capitula lectionum.
In the case of the Bible these are not original to the scriptural authors, and the division of a Biblical book into chapter and verse is also not original. The capitula were developed later for the aid of readers, before the modern consistent system of numbering was established. They are attested from the third century, but may originate earlier. Essentially there might be a sort of table of contents showing where each distinct chunk of narrative could be found in the following text, or else a series of marginal notes to the same effect. Texts of this kind were also added to the works of other writers, in the same way. Some authors would have originated their own summaries.
One example Houghton points to is the Codex Corbeiensis (Paris: Bibliothèque nationale de France, Latin 17225), a manuscript of the eighth to tenth centuries. Before the text of each gospel there appears a list of notable excerpts, such as number 8 for Mark,
in synagogam hominem habente manum aridam sanavit
or "in the synagogue he healed a man who had a withered hand". This happens a few pages later in the actual text, at the point noted with the number 8 (in the third column). It is not obvious from the black-and-white image but the first line of the numbered passage, "et introivit iterum", is also highlighted in red for ease of navigation. Note that this demonstrates that what's in the capitula is not the first line of each passage (the "incipit"), but a summary of the content.
These days, we call this passage "Mark 3:1-6", but modern Bible editions will often precede it with a similar heading, such as "The Man with a Withered Hand" (NRSV) or "The withered hand is healed" (Geneva Bible).