This answer is essentially a summary of a shiur by Rav Moshe Lichtensteinשליט"א, (of Yeshivat Har Etzion) that I found (by Googling) here.
Firstly, the source of this Haftara - Machar Chodesh - is from the Gemara in Megila 31a:
ראשחדששחללהיותבשבתמפטיריןוהיהמדיחדשבחדשוחללהיותבאחדבשבתמאתמולמפטיריןויאמרלויהונתןמחרחדש
From the criteria of this Haftara - i.e. tomorrow is Rosh Chodesh - it seems that the Haftarot not only connect to the day or weekly Parsha, but to the Jewish life cycle in general.
So we're announcing that we're at the end of the month and it's time to prepare for the new month.
This Haftara not only announces this with its opening words, but also with its message; Jonathan and David renewing the commitment to each other. This should be a reminder that Rosh Chodesh is a time for Teshuva and renewing our commitment to Torah & Mitzvot.