Targum translates נוית as בית אולפנא, a school. רד״ק elaborates:
This was David’s first contact with the man who anointed him king since that first visit. What would they have talked about? His upcoming responsibilities:
עמלק was pretty much wiped out (though not enough, as we will see). חז״ל see a hint of their conversation in the name of the place they sat, נוית, seeing it as the plural of נוה.
To review recent history, about 13 years before, the משכן in שילה had been destroyed and the ארון taken by the פלישתים. The משכן was rebuilt (though only of curtains, not real walls) with the central מזבח in נב (just north of Jerusalem), and the ארון eventually recovered and placed in גבעת קרית יערים, the modern Telz-Stone. Note that both cities are in בנימין. But this was clearly temporary; בני ישראל had a responsibility to build a מקדש, a permanent place to spread the word of ה׳ to the world (we will deal more with the difference between a משכן and a מקדש later). They had a tradition that the מקדש would be built in בנימין, but not where:
So חז״ל saw נוית as the place to study about the נוה, the equivalent of today’s Temple Institute:
Rabbi Shulman points out that there was a political reason for situating the מקדש in Jerusalem, on the border between יהודה and בנימין: it would help unite the country that still saw itself as יהודה and ישראל, separately. And the political center of the kingdom needs to be part of the Temple complex, just like the Sanhedrin, since the king acts as judge.
The רמב״ם sees this political side to the location of the מקדש as the reason that the Torah doesn’t specify it:
In fact, looking for the place of the מקדש was seen as a מצוה:
Most of this analysis is from Hirsch.
חז״ל saw this as the beginning of David’s single-minded focus on building the בית המקדש, when he swore that he would not rest until it was built:
The perek is composed of two complementary verses, one describing David’s oath, the second describing ה׳'s. David’s part is itself composed of two parts, the first being the oath itself. ה׳ is described as אביר יעקב, since יעקב is the first to make such an oath to build a מקדש:
אביר is an unusual word. It means “strong one, hero”, but in general it is spelled with a patach under the aleph and a dagesh in the bet, אַבִּיר. But when it refers to ה׳, it is always spelled with a chataf-patach and without the dagesh, אֲבִיר. I have not found an explanation why. It is also only used with the name יעקב (once with ישראל).
David uses the term משכנות, in the plural, since the משכן consists of three parts that at that time were separated: the קודש הקדשים, with the ארון, that was in קרית יערים; the קודש, with the מנורה and שולחן, that was in נב; and the חצר, with the מזבח. While there must have been a מזבח in נב (though it is not explicitly mentioned), מזבחות were permitted throughout ארץ ישראל (called במות), so effectively all of ארץ ישראל was the חצר. David promises not to rest until he can unite them all.
The second half of David’s part is a prayer that the oath be fulfilled. The ארון, the source of ה׳'s voice in this world, as in (שמות כה:כב) ונועדתי לך שם ודברתי אתך מעל הכפרת מבין שני הכרבים אשר על ארון העדת את כל אשר אצוה אותך אל בני ישראל׃), has been in אפרת, a poetic term for אפרים (the location of שילה) and in קרית יערים, here called שדי יער. But those were only temporary; now is the time for it to finally rest, contrasting to Moshe’s prayer the first time the ארון moved:
Hirsch points out that the phrase הדם רגליו also implies resting after a journey.
And שלמה repeats the prayer when he finally builds the בית המקדש, and, looking ahead in our perek, ה׳ reassures David that He will listen to that prayer:
The second half of the perek is ה׳'s oath to David, which is explicitly discussed when ה׳ tells him that he will be unable to build the בית המקדש:
ה׳'s part starts with a restatement of this promise, making it clear that it is conditional on David’s descendants keeping the Torah (no aposiopesis here!) then the reassurance mentioned above. All-in-all, this is a שיר המעלות, a song sung on the steps of the בית המקדש, about the importance of the בית המקדש.