The superscript, or heading, for this Psalm is:

Of David;
when he altered his senses before Abimelech,
who drove him away, and he departed.

Concerning the mention of Abimelech, according to 1 Samuel 21:10-15, David pretended to be insane before the Philistine king, “Achish,” king of Gath, not Abimelech. The apparent contradiction can be cleared up by understanding that the name “Abimelech” means “My father is king,” and it was apparently a dynastic title for kings of that line. That explains why “Abimelech” dealt with Abraham (Gen. 20:2) and with Isaac (Gen. 26:1). The title was still being used in the area even during David’s time.