Abner kills Asahel. From Johann Christoff Weigel, 1695
David was made King over Judah, but some of Saul's family and followers did not like this. For instance, a general named Abner went and installed Saul's son Ishbosheth as the king over Jezreel,Gilead, Ephraim, Benjamin, and over the Ashurites. Abner was the captain of the deceased Saul's army.
Abner then took some men and went down to a place called Gibeon, where some of the newly installed King David's followers sought him out, under a general named Joab. It seems that Joab and Abner were trying to negotiate some sort of compromise. The meeting was an odd one, because at some point Abner said, "Let the young men rise, and play before us." Joab told them to arise, and the "game" they played was something more like the Romans' version of decimation, but instead all died. Or maybe the King James Bible wasn't written clearly, and this was just meant to be more like a gladiatorial fight.
Anyhow, twelve young men for each side got up, grabbed the head of his opponent and then thrust his sword into his opponent's side, so that all 24 of them fell down in unison.
A battle ensued between the two armies, and after realizing that the battle would be won by Joab, Abner tries to make his escape. One of Joab's lieutenants, Asahel, sees this escape attempt and pursues Abner. , Abner winds up having to kill Asahel (pictured above) with the blunt end of his spear.
My personal thoughts on this chapter is just to marvel once again at level of detail offered by the book's authors, and also how interesting it is for us to have this little window into the minds of these Bronze Age people.