The “Song of the Bow” is David’s lament over Saul and Jonathan after their death. It is introduced as a song to be taught to Judah and recorded. See 2 Samuel 1:17–18.
After hearing of Saul and Jonathan’s deaths, David responds by composing a formal mourning song for them. The narrator presents this as a specific, recognized lament, not a private outburst. David also orders that the people of Judah be taught “the Bow,” apparently the title or identifying phrase for the song. These verses introduce the poem that follows (1:19–27) by explaining why it exists and how it was transmitted. The story has just reported the deaths of Saul and Jonathan and David’s immediate acts of grief and inquiry.
These verses present David’s grief as a crafted, public act. The narrator says David produced a formal lament over both Saul and Jonathan, and he signals that it was meant to be remembered and passed on, not kept private (2 Samuel 1:17–18). Two features underline this public purpose.
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with 2 Samuel 1:17-18, then read the surrounding section so the answer stays connected to the passage's flow.
17David lamented with this lamentation over Saul and over Jonathan his son
18(and he bade them teach the children of Judah [the song of] the bow: behold, it is written in the book of Jashar):