This Mishnah (Chapter 14, Mishnah 7) deals with the period following Shiloh, and to understand it, we will first introduce the historical background. Previously, the Mishkan resided in Shiloh, where it stood for three hundred and sixty-nine years. At the end of that period, a war broke out with the Philistines, and the Jewish people took the Holy Ark out of the Mishkan to the battlefield - and the Philistines captured the Ark. This was a fatal blow to Shiloh: when Eli the kohen, the Kohen Gadol, heard that the Ark had been captured, he fell backward, broke his neck, and died. With this, the period of Shiloh ended.
The Mishkan in Nov and the Ark in Kiryas Ye'arim:
Shmuel the prophet moved the Mishkan to the city of Nov. The Jewish people recovered the Ark, but did not return it to the Mishkan in Nov, which was not a fortified and secure city. Instead, they brought it up to a place called Kiryas Ye'arim (modern-day Telz-Stone, outside Jerusalem). From this point on, the Mishkan and the Ark were no longer connected to each other, and even the Mishkan did not stand in a permanent location: Nov was a relatively temporary place, during the period when Shaul still reigned and David was in a transitional period.
Shaul eventually destroyed the city of Nov and killed its inhabitants, including kohanim. Shmuel moved the Mishkan from Nov to Giv'on, where it stood until King Shlomo, the son of David, built the Beis HaMikdash in Jerusalem. The period of Nov and Giv'on together lasted fifty-seven years. The Ark itself, after twenty years, was moved from Kiryas Ye'arim to David's new city - the City of David, south of Jerusalem - and remained there until the Beis HaMikdash was built.
The language of the Mishnah:
"Ba'u leNov uleGiv'on - hutru habamos" - As long as the Mishkan was in Nov and Giv'on, the bamos, private altars, became permitted once again. This is because the verse specified to Moshe Rabbeinu that the prohibition of bamos would apply in the "menuchah" - which is Shiloh - and in the "nachalah", the permanent inheritance - which is Jerusalem; and between the two, during those fifty-seven years of Nov and Giv'on, bamos were permitted.
"Kodshei kodashim ne'echalim lifnim min hakla'im" - As before: most holy offerings that were brought in Nov or Giv'on were eaten within the curtains that surrounded the Mishkan erected there.
"Vekodashim kalim bechol arei Yisrael" - Offerings of lesser holiness were eaten anywhere in the Land of Israel.
Here the Mishnah uses the term "cities of Israel" rather than "anywhere," as in the two previous Mishnahs, even though the meaning is identical. The difference in terminology stems from the reality at the time: during the period of Gilgal, the cities of Israel had not yet been established, as they were still engaged in conquering and dividing the land; whereas now the land was settled, it had cities, and every city was valid for eating offerings of lesser holiness.
The law is the same regarding ma'aser sheni. The Mishnah does not mention ma'aser sheni here, because its novel halachah was already stated regarding the period of Shiloh; however, the law is exactly the same - every city and location in the Land of Israel is valid for offerings of lesser holiness as well as for ma'aser sheni.
In summary: In this section we learned the history of the Mishkan after the destruction of Shiloh - its relocation to Nov and from there to Giv'on, and its separation from the Ark, which was brought up to Kiryas Ye'arim and, after twenty years, to the City of David. During those fifty-seven years of Nov and Giv'on, which were neither "menuchah" nor "nachalah," bamos were permitted; most holy offerings were eaten within the curtains, and offerings of lesser holiness - as well as ma'aser sheni - in all the cities of Israel.