When Shabbat is the day before Rosh Chodesh, there is a special Haftarah that is read instead of the regular Haftarah for that Parsha. The text of Machar Chodesh is from Shmuel I, describing a young David trying to figure out where he stands with King Shaul.
Linear annotated translation of the Haftarah of Machar Chodesh
There is a long and complicated back story which I tried to summarize in the introduction. Here is a painting by Rembrandt that shows one of the scenes that preceded the story of the Haftarah itself.
If tomorrow is Rosh Chodesh, what is tonight? Darkest Hour